{"id":"W1661817784","doi":"10.1023/a:1017501925328","title":"On fine gradings and their symmetries","year":2001,"lang":"en","type":"article","venue":"Czechoslovak Journal of Physics","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal; Université du Québec à Montréal","funders":"","keywords":"Homogeneous space; Pure mathematics; Prime (order theory); Mathematics; Physics; Unification; Finite field; Mathematical physics; Algebra over a field; Discrete mathematics; Combinatorics; Computer science; 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":[0.0002273446,0.0001609558,0.000330997,0.000120812,0.0000788969,0.00003217312,0.0001508933,0.00004778447,0.00002361966],"category_scores_gemma":[0.000553599,0.0001118922,0.0001195276,0.0003950463,0.00006824145,0.0002385997,0.00003299496,0.0003040566,0.000007388656],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002818928,"about_ca_system_score_gemma":0.00001942879,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":2.205951e-7,"about_ca_topic_score_gemma":4.134001e-7,"domain_scores_codex":[0.9991912,0.00002256292,0.0003040895,0.0001022832,0.0001958905,0.0001839609],"domain_scores_gemma":[0.9985651,0.0006384929,0.0003355487,0.0001615751,0.0001982538,0.0001010572],"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":[0.0001693914,0.0003935356,0.001182127,0.00008360357,0.0001941863,0.00007500259,0.001122781,0.00002668705,0.003187863,0.8307172,0.00685155,0.155996],"study_design_scores_gemma":[0.000557219,0.0002980552,0.0001983872,0.0001153654,0.00002703612,0.000147881,0.0002146915,0.00002231696,0.01406022,0.9820754,0.002154824,0.0001286253],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9500487,0.0004404416,0.04800399,0.0003406786,0.0001911866,0.00005471026,0.000003583134,0.00001945719,0.0008971788],"genre_scores_gemma":[0.9964855,0.000171767,0.00243607,0.0001981346,0.0004316933,6.073092e-7,4.682076e-7,0.00002494045,0.0002507661],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1558674,"threshold_uncertainty_score":0.4562832,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02932191870283384,"score_gpt":0.2880766426900996,"score_spread":0.2587547239872657,"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."}}