{"id":"W3124993320","doi":"10.1090/proc/15465","title":"A generalization of Winternitz’s theorem and its discrete version","year":2021,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Centroid; Convex body; Generalization; Line (geometry); Regular polygon; Mathematics; Combinatorics; Plane (geometry); Mathematical analysis; Geometry; Convex hull","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001390945,0.0005470539,0.0006480205,0.00131164,0.001059176,0.001365318,0.001550817,0.0008335885,0.009115824],"category_scores_gemma":[0.003747777,0.0002397753,0.001150852,0.001202778,0.003914037,0.003997257,0.002536074,0.002667952,0.001042278],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001713053,"about_ca_system_score_gemma":0.0006066279,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002791649,"about_ca_topic_score_gemma":0.001944344,"domain_scores_codex":[0.9987349,0.0001567357,0.00005199042,0.0005012709,0.000379003,0.0001760698],"domain_scores_gemma":[0.9982623,0.0008025516,0.0001972892,0.000297134,0.0002813249,0.000159359],"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":[0.00004950461,0.00001926867,0.0007785087,0.0001179558,0.00002131753,0.0001263396,0.0002003165,0.004293167,0.0026383,0.960323,0.00467858,0.02675371],"study_design_scores_gemma":[0.00002859406,0.00007619487,0.002057063,0.00003823726,0.00001624183,0.0004935918,0.0001322621,0.02105594,0.001817712,0.9328811,0.0413812,0.00002206685],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09136041,0.003965294,0.7317672,0.008013065,0.001171752,0.0001047714,0.0009750075,0.0002174387,0.1624251],"genre_scores_gemma":[0.800994,0.00369277,0.1456896,0.002774526,0.001848528,0.0002601891,0.000754742,0.0002729932,0.04371263],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009115824,"threshold_uncertainty_score":0.03049546,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02403529596382924,"score_gpt":0.2904514316363737,"score_spread":0.2664161356725445,"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."}}