{"id":"W2952239370","doi":"10.48550/arxiv.math/0506336","title":"Rearrangement inequalities for functionals with monotone integrands","year":2005,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Metal complexes synthesis and properties","field":"Medicine","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Monotone polygon; Inequality; Mathematics; Pure mathematics; Mathematical economics; Applied mathematics; Mathematical analysis; Geometry","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004902025,0.0003651596,0.0007621126,0.0001395996,0.000103762,0.00003792739,0.0001546758,0.0001858808,0.0008005548],"category_scores_gemma":[0.0001483948,0.0002354071,0.0002615974,0.00006118337,0.0001031615,0.00005400732,0.0001585469,0.0003878844,0.00007778926],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009174379,"about_ca_system_score_gemma":0.0001598114,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001531836,"about_ca_topic_score_gemma":0.00004831034,"domain_scores_codex":[0.9983118,0.00006422931,0.0004810863,0.0005012585,0.0003457206,0.0002959592],"domain_scores_gemma":[0.998643,0.0001368297,0.0001945474,0.0006196736,0.0002915113,0.0001143981],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"not_applicable","study_design_scores_codex":[0.02934101,0.00248573,0.7265027,0.01374634,0.009140355,0.00005399498,0.008693382,0.0006490428,0.08938099,0.006387817,0.05442723,0.05919143],"study_design_scores_gemma":[0.005425095,0.002766606,0.2499499,0.004123047,0.002001531,0.00005625476,0.001884748,0.0005431413,0.06190755,0.001647247,0.6680771,0.001617817],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9819968,0.003014632,0.002349518,0.003252614,0.0003579809,0.001309147,0.00007791758,0.0001192641,0.007522177],"genre_scores_gemma":[0.9711578,0.0003471738,0.002982839,0.001110642,0.001129924,0.0008500314,0.0002756184,0.0000690916,0.02207682],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6136498,"threshold_uncertainty_score":0.9599621,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2089919902841936,"score_gpt":0.3288607035343197,"score_spread":0.1198687132501261,"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."}}