{"id":"W2113968058","doi":"10.1112/s0010437x11005343","title":"Poincaré inequalities, embeddings, and wild groups","year":2011,"lang":"en","type":"article","venue":"Compositio Mathematica","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":62,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Microsoft Research; David and Lucile Packard Foundation; National Science Foundation","keywords":"Metric space; Convexity; Embedding; Metric (unit); Fixed point; Group (periodic table); Convex metric space; Variety (cybernetics)","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001977124,0.0004525101,0.0005207733,0.001751967,0.0009649934,0.001669462,0.0006692296,0.0007423554,0.004038877],"category_scores_gemma":[0.006286172,0.0002018436,0.0005564414,0.0007071155,0.004149369,0.003473901,0.002627256,0.001469899,0.0002600109],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001243404,"about_ca_system_score_gemma":0.0004011803,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009775944,"about_ca_topic_score_gemma":0.0007048884,"domain_scores_codex":[0.9990343,0.0003393784,0.00005382317,0.0001848129,0.0002439737,0.0001436672],"domain_scores_gemma":[0.9968807,0.001637954,0.0005340323,0.0002891016,0.000385165,0.0002730886],"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":[0.000009789767,0.000005542132,0.0003724009,0.00001498655,0.00000644689,0.00005518787,0.00006750367,0.00178102,0.0008333405,0.9950126,0.0002620741,0.001579024],"study_design_scores_gemma":[0.00001265506,0.00003198538,0.0009668102,0.00001129692,0.000005759007,0.00009837384,0.00009302086,0.0193393,0.0009640622,0.9769351,0.001528634,0.00001290265],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7045877,0.001672172,0.2257886,0.003375116,0.0001648484,0.00005785562,0.0002847146,0.000105223,0.06396387],"genre_scores_gemma":[0.9896979,0.0002846055,0.007456786,0.0001410452,0.0001145284,0.00004088168,0.0001084628,0.00001555887,0.002140125],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004038877,"threshold_uncertainty_score":0.01351136,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0725326724035067,"score_gpt":0.280925281786253,"score_spread":0.2083926093827463,"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."}}