{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0006541502,0.0005039886,0.0006783493,0.001106183,0.0001754258,0.000105107,0.000876408,0.0006972768,0.0004778639],"category_scores_gemma":[0.0007965889,0.0005316051,0.0003533677,0.002691078,0.0002785831,0.0002026557,0.001165123,0.00113019,0.0004062956],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002597379,"about_ca_system_score_gemma":0.0003220189,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002406403,"about_ca_topic_score_gemma":0.00006229118,"domain_scores_codex":[0.9976288,0.0001372892,0.0004142797,0.00103461,0.0001958717,0.0005891682],"domain_scores_gemma":[0.9973088,0.0006858157,0.0004615349,0.0009831276,0.0003679023,0.0001928181],"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":[0.00004791094,0.0002824875,0.0009304124,0.002971397,0.0007044004,0.0004262736,0.0006157176,0.02084432,0.0000132449,0.9507232,0.02219553,0.0002451126],"study_design_scores_gemma":[0.0007367343,0.00006606887,0.0002139756,0.0005130301,0.0003831317,0.00001147304,0.001478376,0.004236173,0.00005884988,0.988623,0.002766577,0.0009126422],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.543044,0.001325318,0.3855728,0.001230931,0.005143825,0.00337424,0.001286231,0.00354067,0.05548194],"genre_scores_gemma":[0.9569529,0.0005762675,0.000824542,0.0001437345,0.0001711336,0.000003125245,0.00007128024,0.00008584144,0.0411712],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4139089,"threshold_uncertainty_score":0.9997135,"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."}}