{"id":"W1993495670","doi":"10.1007/s00209-002-0479-6","title":"On a separation property of positive definite functions on locally compact groups","year":2003,"lang":"en","type":"article","venue":"Mathematische Zeitschrift","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Separation (statistics); Property (philosophy); Locally compact space; Separation property; Positive-definite matrix; Pure mathematics; Statistics; Eigenvalues and eigenvectors","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":[],"category_scores_codex":[0.0007840941,0.0003618931,0.0005444204,0.0002372155,0.0002258392,0.0000571611,0.0002420502,0.0001604915,0.0005835255],"category_scores_gemma":[0.002138921,0.000239075,0.0001641908,0.000488927,0.0001318716,0.00023857,0.00003861805,0.0004966385,0.0008611137],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000289632,"about_ca_system_score_gemma":0.0001338106,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008543276,"about_ca_topic_score_gemma":0.00001502733,"domain_scores_codex":[0.9973053,0.0003650639,0.000619919,0.0004497607,0.000802371,0.0004575497],"domain_scores_gemma":[0.9971077,0.001421783,0.0002428021,0.0007544609,0.0003061435,0.0001670909],"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":[0.0001673041,0.0009581559,0.00007082456,0.0001791482,0.0001103409,0.00001215676,0.0007905592,0.0003077399,0.004160463,0.9874828,0.005439813,0.0003206283],"study_design_scores_gemma":[0.01035039,0.0103363,0.002330721,0.004201609,0.0004758804,0.0003426117,0.002538438,0.005737932,0.3739112,0.5656707,0.02072958,0.003374605],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3610542,0.00009542824,0.1109395,0.0004583795,0.0002181948,0.002590877,0.0001542258,0.0003198446,0.5241693],"genre_scores_gemma":[0.9840735,0.000006480318,0.01208181,0.0001852564,0.00003319385,0.00008168066,0.00002033779,0.00009195421,0.003425753],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6230193,"threshold_uncertainty_score":0.9999169,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0504395893192673,"score_gpt":0.3455622898568379,"score_spread":0.2951227005375706,"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."}}