{"id":"W6979316454","doi":"","title":"The $m$th order Orlicz projection bodies","year":2025,"lang":"en","type":"article","venue":"arXiv (Cornell University)","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Centre Scientifique et Technique du Bâtiment; National Natural Science Foundation of China; Chongqing Municipal Education Commission; Natural Science Foundation of Chongqing; Chongqing Science and Technology Commission","keywords":"Projection (relational algebra); Convexity; Convex set; Convex body; Regular polygon; Convex function; Function (biology); Affine transformation; Order (exchange)","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004966531,0.0008254223,0.0005270289,0.001320703,0.001193545,0.00242388,0.001078482,0.0009989233,0.01260613],"category_scores_gemma":[0.001396595,0.0003083645,0.0007814082,0.0005976377,0.003092888,0.003332542,0.002283831,0.002315212,0.002338388],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001048461,"about_ca_system_score_gemma":0.001150066,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001260011,"about_ca_topic_score_gemma":0.001025884,"domain_scores_codex":[0.9993504,0.000086328,0.00002341994,0.0001806829,0.0001861874,0.0001729135],"domain_scores_gemma":[0.9995491,0.00006777865,0.00007482849,0.00006424006,0.0001293774,0.0001146067],"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":[0.00001702858,0.00001513099,0.0001549544,0.00002263819,0.000003669345,0.00005571907,0.0001189537,0.0008525055,0.001371903,0.9904538,0.001270622,0.005663097],"study_design_scores_gemma":[0.00002114015,0.00009285712,0.0008020473,0.0000339445,0.00000903307,0.0003381082,0.0002692353,0.04048016,0.003950709,0.930315,0.02363273,0.00005511092],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.1730639,0.0007411701,0.6148128,0.001482815,0.0005738551,0.0001899227,0.0006696422,0.000486725,0.2079791],"genre_scores_gemma":[0.7498833,0.00119864,0.1529822,0.0009907983,0.0007440922,0.0003464129,0.0008301728,0.0004750095,0.09254926],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.01260613,"threshold_uncertainty_score":0.04217166,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1077257537904689,"score_gpt":0.2351966443207352,"score_spread":0.1274708905302663,"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."}}