{"id":"W4400460376","doi":"10.5802/crmath.577","title":"Essential dimension of symmetric groups in prime characteristic","year":2024,"lang":"en","type":"article","venue":"Comptes Rendus Mathématique","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Combinatorics; Mathematics; Dimension (graph theory); Prime (order theory); Integer (computer science); Finite field; Field (mathematics); Group (periodic table); Prime number; Polynomial; Discrete mathematics; Physics; Pure mathematics; Mathematical analysis; Quantum mechanics","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":[0.001120587,0.0002318627,0.0005102398,0.0008911113,0.00003698192,0.00007668456,0.0003570519,0.0001708164,0.0007827529],"category_scores_gemma":[0.0007735667,0.0002074434,0.0001197314,0.001156806,0.0001094054,0.0001654609,0.0002454059,0.000521575,0.0003539706],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001192721,"about_ca_system_score_gemma":0.00008852789,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002107896,"about_ca_topic_score_gemma":0.000006453188,"domain_scores_codex":[0.9978216,0.0003069455,0.0006963462,0.0003621298,0.0004321261,0.0003808775],"domain_scores_gemma":[0.9971903,0.001995924,0.0001268253,0.000520154,0.00008182361,0.00008498508],"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":[0.00009266559,0.0005856905,0.0009889603,0.003324207,0.00010483,0.0003069388,0.002061199,0.000004435168,0.0797296,0.9040654,0.003166856,0.005569176],"study_design_scores_gemma":[0.0013028,0.0004955569,0.01646222,0.004164709,0.000125294,0.0002313035,0.0003281972,0.05173232,0.07144324,0.8514082,0.001241267,0.001064911],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9924414,0.001041779,0.002551047,0.0001253857,0.0003322128,0.0004579663,0.0000298024,0.000207133,0.002813302],"genre_scores_gemma":[0.9965933,0.0001003918,0.002678928,0.00001140485,0.00008806144,0.00004617791,0.00002636768,0.00006523373,0.0003901655],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05265727,"threshold_uncertainty_score":0.8570595,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03818796757351079,"score_gpt":0.3310853126787894,"score_spread":0.2928973451052787,"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."}}