{"id":"W3176060828","doi":"10.15488/14685","title":"Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity","year":2021,"lang":"en","type":"preprint","venue":"Zurich Open Repository and Archive (University of Zurich)","topic":"Risk and Portfolio Optimization","field":"Decision Sciences","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Universität Bielefeld; University of Waterloo","keywords":"Quasiconvex function; Convexity; Invariant (physics); Quantile; Regular polygon; Mathematics; Mathematical economics; Applied mathematics; Pure mathematics; Economics; Econometrics; Convex analysis; Finance; Convex optimization; Geometry; Mathematical physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.003654104,0.0003139034,0.0007439757,0.0002508007,0.001466075,0.0009635754,0.002519198,0.0002108186,0.0003144963],"category_scores_gemma":[0.0002205461,0.0002611826,0.0002594852,0.000573491,0.000433133,0.0005797568,0.005778112,0.0004833281,0.00004216421],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004580916,"about_ca_system_score_gemma":0.0004364241,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003188082,"about_ca_topic_score_gemma":0.001741926,"domain_scores_codex":[0.9949248,0.002001133,0.0004579398,0.001158171,0.00117962,0.0002782791],"domain_scores_gemma":[0.994952,0.00195957,0.0008119122,0.00135246,0.0006124689,0.0003116204],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"not_applicable","study_design_scores_codex":[0.002103019,0.001441293,0.04130229,0.0001751012,0.001724276,0.001550248,0.08704298,0.04417374,0.001794559,0.08165813,0.7250977,0.01193666],"study_design_scores_gemma":[0.002141951,0.0005850317,0.1448631,0.0004189741,0.0007349095,0.0002061865,0.0502044,0.008914928,0.001154829,0.06110879,0.727863,0.001803855],"study_design_candidate":"not_applicable","study_design_consensus":"not_applicable","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4365481,0.001527762,0.2055109,0.01312645,0.005386813,0.004444103,0.0009351644,0.0001092465,0.3324115],"genre_scores_gemma":[0.956032,0.0009700356,0.02317712,0.0008451602,0.0002379229,0.00000658631,0.0001727179,0.00002724014,0.01853121],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.519484,"threshold_uncertainty_score":0.999984,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06482790382696972,"score_gpt":0.2897319847149908,"score_spread":0.2249040808880211,"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."}}