{"id":"W4323556013","doi":"10.48550/arxiv.2303.02294","title":"Reverse isoperimetric problems under curvature constraints","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Isoperimetric inequality; Mathematics; Ball (mathematics); Inscribed figure; Regular polygon; Conjecture; Combinatorics; Incircle and excircles of a triangle; Lambda; Curvature; Convex polytope; Minimal surface; Mathematical analysis; Bounded function; Geometry; Convex set; Physics; Convex optimization","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":[0.002213186,0.001137766,0.001111666,0.001405493,0.001288566,0.00209689,0.002530992,0.002261149,0.005492316],"category_scores_gemma":[0.01261791,0.0008040607,0.001430148,0.0009898074,0.002953431,0.006909582,0.004082374,0.005092846,0.0006158818],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001860254,"about_ca_system_score_gemma":0.0006456616,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001980196,"about_ca_topic_score_gemma":0.001415676,"domain_scores_codex":[0.998171,0.0005057458,0.00008678977,0.0005284895,0.0004675364,0.0002405662],"domain_scores_gemma":[0.9935721,0.004183279,0.0007392865,0.0005204615,0.0005336523,0.0004511539],"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":[0.00006476575,0.00003381115,0.001173791,0.0001490187,0.00003169416,0.0001655867,0.0002393071,0.03453958,0.001441379,0.946464,0.001987911,0.01370901],"study_design_scores_gemma":[0.00002195372,0.00005752294,0.000815166,0.00004170664,0.00002057554,0.0002423047,0.0002043676,0.168228,0.001844966,0.8223078,0.006183964,0.00003155823],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.1904922,0.002015817,0.7638041,0.003915501,0.0001977063,0.00009679228,0.0005815002,0.0002091273,0.0386873],"genre_scores_gemma":[0.7947533,0.001693237,0.1760662,0.0005796807,0.0005440125,0.0002098918,0.001173785,0.0002533947,0.02472646],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.005492316,"threshold_uncertainty_score":0.01837367,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.3133147368554371,"score_gpt":0.2572758389092318,"score_spread":0.05603889794620531,"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."}}