{"id":"W2011217413","doi":"10.4153/cjm-2003-040-x","title":"Some Convexity Results for the Cartan Decomposition","year":2003,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"Laurentian University","funders":"","keywords":"Mathematics; Pure mathematics; Abelian group; Product (mathematics); Decomposition; Convexity; Type (biology); Cartan decomposition; Simple (philosophy); Measure (data warehouse); Regular polygon; Set (abstract data type); Polar decomposition; Algebra over a field; Geometry","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":[0.001319816,0.0006224259,0.0006887797,0.002222886,0.001883675,0.003115405,0.0005881565,0.0004625141,0.004417434],"category_scores_gemma":[0.002469858,0.0004396059,0.0008278401,0.00145098,0.002552764,0.002335242,0.001506846,0.001652471,0.000562016],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001877187,"about_ca_system_score_gemma":0.0005431465,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003639718,"about_ca_topic_score_gemma":0.002555945,"domain_scores_codex":[0.9990653,0.0002102755,0.0000377465,0.0001380627,0.0003842441,0.0001644257],"domain_scores_gemma":[0.9983551,0.0006915155,0.0001789881,0.0001274489,0.0004119937,0.0002348936],"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":[0.00001064372,0.000007457814,0.0003185705,0.00001604404,0.000009209331,0.00009967318,0.0001162003,0.001667348,0.0005750444,0.9939811,0.001237501,0.001961189],"study_design_scores_gemma":[0.000007462418,0.00001244825,0.001231103,0.00003262691,0.00001416861,0.0001919209,0.0001625671,0.03606146,0.001178185,0.9535905,0.007496217,0.00002129357],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4772926,0.003249443,0.2596978,0.002751791,0.0002430292,0.0000667432,0.0009352025,0.0002028864,0.2555605],"genre_scores_gemma":[0.9663511,0.0008837489,0.01777912,0.0002543707,0.0003008649,0.00005171827,0.0005993895,0.000128721,0.01365102],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004417434,"threshold_uncertainty_score":0.01477784,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06209498963574948,"score_gpt":0.3312132769208871,"score_spread":0.2691182872851376,"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."}}