{"id":"W2725281740","doi":"10.5539/jmr.v9n4p23","title":"Sign of Permutations Induced by Anick and Nagata-Anick Automorphisms over Finite Fields","year":2017,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Japan Society for the Promotion of Science","keywords":"Mathematics; Automorphism; Sign (mathematics); Finite field; Prime (order theory); Combinatorics; Inner automorphism; Automorphism group; Field (mathematics); Discrete mathematics; Pure mathematics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003327686,0.00008100758,0.0002401525,0.0002537244,0.0003549159,0.0003381645,0.00134142,0.00007570497,0.00005864063],"category_scores_gemma":[0.001084078,0.00006430339,0.0001000029,0.0001723688,0.0001673094,0.0004820716,0.000374339,0.0004574807,0.00000552886],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001503053,"about_ca_system_score_gemma":0.0001048145,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008731315,"about_ca_topic_score_gemma":0.000003181101,"domain_scores_codex":[0.9983778,0.0001541309,0.0004104644,0.0001181452,0.0007366249,0.0002028584],"domain_scores_gemma":[0.9972829,0.001118293,0.0004431508,0.0006181583,0.0004207974,0.0001166772],"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":[0.00008069356,0.001483573,0.0009122958,0.0005737076,0.0004926581,0.0001296968,0.01991703,0.00005277793,0.09307995,0.8331948,0.02245849,0.02762435],"study_design_scores_gemma":[0.001793498,0.00195809,0.004798231,0.0005542266,0.00005873983,0.0001668222,0.001006042,0.04628891,0.01918309,0.9220135,0.001819655,0.0003592442],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8494,0.000185796,0.1462655,0.001767629,0.0001349085,0.0001396413,0.00000671246,0.00001097858,0.002088822],"genre_scores_gemma":[0.9877979,0.00006101982,0.01193368,0.00002287844,0.00003356877,0.000001736378,1.884901e-7,0.000006547099,0.0001425285],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1383978,"threshold_uncertainty_score":0.3260928,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.131082758862121,"score_gpt":0.4011813500062456,"score_spread":0.2700985911441246,"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."}}