{"id":"W1969719817","doi":"10.1007/s11856-012-0135-8","title":"Multiple commutator formulas","year":2012,"lang":"en","type":"article","venue":"Israel Journal of Mathematics","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Commutator; Mathematics; Commutator subgroup; Combinatorics; Congruence (geometry); Algebra over a field; Group (periodic table); Pure mathematics; Normal subgroup; Physics; 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":[0.003614563,0.0002118022,0.0005470864,0.0002491795,0.0001057541,0.00005361078,0.0006117478,0.0001193062,0.0001604757],"category_scores_gemma":[0.003965263,0.0001599948,0.0002663553,0.0002196796,0.0001071112,0.0003841805,0.0001448936,0.000521677,0.0001627639],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001086307,"about_ca_system_score_gemma":0.00006534487,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001919836,"about_ca_topic_score_gemma":0.000003359454,"domain_scores_codex":[0.997376,0.0001617903,0.0009933085,0.00007122132,0.0008387079,0.0005589364],"domain_scores_gemma":[0.9947191,0.003354467,0.0007474446,0.0004787328,0.0003726247,0.00032759],"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":[0.0002715879,0.007869764,0.02985405,0.002405298,0.0009368012,0.0001464037,0.03498271,0.0000141653,0.0117776,0.8808491,0.0232515,0.007641036],"study_design_scores_gemma":[0.004387151,0.0006772664,0.0008124994,0.0008384365,0.0003010978,0.003766049,0.0199744,0.001963723,0.02114288,0.9302267,0.01506828,0.0008414707],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.967761,0.0004218433,0.02642115,0.0001734214,0.0003844023,0.0002366731,0.00000972523,0.00004262711,0.004549116],"genre_scores_gemma":[0.8479553,0.00002073063,0.1511047,0.00006789029,0.0004047096,0.000003616975,6.8158e-7,0.00006585113,0.0003764978],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1246835,"threshold_uncertainty_score":0.6524399,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1287431090251704,"score_gpt":0.3767892736674631,"score_spread":0.2480461646422927,"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."}}