{"id":"W2032694901","doi":"10.4171/ggd/213","title":"Filling inequalities for nilpotent groups through approximations","year":2013,"lang":"en","type":"article","venue":"Groups Geometry and Dynamics","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":17,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Nilpotent; Approximations of π; Inequality; Nilpotent group; Pure mathematics; Central series; Group (periodic table); Algebra over a field; Mathematical analysis","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":[0.0008404426,0.0002665521,0.0003831382,0.0002369095,0.0003992038,0.000254028,0.0002780457,0.0001934352,0.0001880249],"category_scores_gemma":[0.001003062,0.0002414167,0.0001304043,0.0004707373,0.0001910965,0.0005921763,0.0001959475,0.0002863468,0.00004768958],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000102918,"about_ca_system_score_gemma":0.00002360797,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004777677,"about_ca_topic_score_gemma":0.00002212735,"domain_scores_codex":[0.9980943,0.0001022582,0.0004999422,0.0003831827,0.0003280312,0.000592334],"domain_scores_gemma":[0.9969643,0.002079305,0.0001444731,0.0004587602,0.0002219403,0.0001312511],"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":[0.00002456764,0.0001287448,0.0005670933,0.0005892518,0.00006287659,0.000001209052,0.001104654,0.00002916116,0.00006721618,0.9936717,0.0007072662,0.003046303],"study_design_scores_gemma":[0.0005721786,0.0001432898,0.0003312934,0.00004624538,0.00003454847,0.00001723559,0.004887796,0.09316624,0.00004710921,0.9001061,0.0003377022,0.0003102154],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5695722,0.000142738,0.4258877,0.0004779179,0.000157704,0.0009885023,0.0001603891,0.0001503521,0.00246248],"genre_scores_gemma":[0.9075491,0.00006589276,0.08898553,0.000169521,0.0002214683,0.0005417439,0.0002415016,0.00007792946,0.002147346],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3379769,"threshold_uncertainty_score":0.9844687,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06989512893870684,"score_gpt":0.3187800082975861,"score_spread":0.2488848793588793,"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."}}