{"id":"W4393986007","doi":"10.1007/s10958-024-07079-z","title":"Random Section and Random Simplex Inequality","year":2024,"lang":"en","type":"article","venue":"Journal of Mathematical Sciences","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Section (typography); Simplex; Inequality; Combinatorics; Random compact set; Random element; Discrete mathematics; Pure mathematics; Random variable; Mathematical analysis; Statistics; Computer science","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003645453,0.0009068439,0.001850686,0.003039417,0.001413174,0.003547562,0.00199627,0.001889288,0.01082745],"category_scores_gemma":[0.01568099,0.0009085473,0.001282591,0.002132427,0.004607448,0.007153828,0.003738062,0.004156139,0.0008111217],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002091164,"about_ca_system_score_gemma":0.00105182,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001969747,"about_ca_topic_score_gemma":0.001416757,"domain_scores_codex":[0.9983838,0.0007083412,0.00005728753,0.0002360544,0.0004442276,0.0001704735],"domain_scores_gemma":[0.9857813,0.01054455,0.001015201,0.0006731279,0.001079652,0.0009063232],"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":[0.0000119488,0.000007454884,0.0001402151,0.00001321892,0.00001037061,0.00002371246,0.0000277332,0.002516649,0.0001239147,0.9956868,0.000455861,0.0009819309],"study_design_scores_gemma":[0.0000093091,0.000007461719,0.0001962953,0.00001197609,0.000006406459,0.00004970366,0.00002161048,0.0282026,0.0001024594,0.9704657,0.0009163615,0.00001022183],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1768831,0.004531923,0.7245172,0.01050229,0.0007033409,0.00007203927,0.0005588427,0.0002660241,0.08196547],"genre_scores_gemma":[0.9036721,0.003445063,0.04702932,0.001513483,0.0009445435,0.0001958769,0.0004587221,0.0002894192,0.04245151],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01082745,"threshold_uncertainty_score":0.03622144,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1009857128273334,"score_gpt":0.3835525984457258,"score_spread":0.2825668856183924,"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."}}