{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005119734,0.0002511137,0.0005223293,0.0002062479,0.000153106,0.00008330772,0.000244367,0.0001113773,0.0008648966],"category_scores_gemma":[0.0002108685,0.000206727,0.0001361525,0.0003974058,0.0000977993,0.0001952909,0.0001375498,0.0001787773,0.00008985519],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002738354,"about_ca_system_score_gemma":0.00001538435,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001520564,"about_ca_topic_score_gemma":0.000003932882,"domain_scores_codex":[0.9984878,0.00007140292,0.0005134546,0.0002945552,0.0003158456,0.0003168891],"domain_scores_gemma":[0.9986842,0.0003805349,0.0001998247,0.000484714,0.00009371004,0.0001570724],"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":[0.00001825611,0.0004221494,0.0003980358,0.0004232222,0.0002108129,0.00002274618,0.009241709,1.155762e-7,0.0002620477,0.982093,0.006224457,0.0006834497],"study_design_scores_gemma":[0.0005284047,0.0001362044,0.0009199767,0.0002059865,0.0003556459,0.0001396845,0.001631972,0.0009030844,0.0007283871,0.9926203,0.00133724,0.000493151],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8310628,0.0006068449,0.04770531,0.0002299138,0.0001312598,0.000460853,0.00001972526,0.0003406107,0.1194427],"genre_scores_gemma":[0.9256783,0.00002265919,0.07305147,0.0001778878,0.00007777365,0.00003054809,0.0000095591,0.00003899813,0.0009128518],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1185298,"threshold_uncertainty_score":0.9470012,"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."}}