{"id":"W4403199740","doi":"10.4171/ggd/835","title":"Amenability of finite energy path and loop groups","year":2024,"lang":"en","type":"article","venue":"Groups Geometry and Dynamics","topic":"Mathematics and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"","keywords":"Loop (graph theory); Mathematics; Path (computing); Energy (signal processing); Group (periodic table); Pure mathematics; Topology (electrical circuits); Discrete mathematics; Combinatorics; Statistics; Computer science; Physics; Computer network","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":[0.000303395,0.0001453532,0.0002547156,0.0001252065,0.00007195811,0.00006089531,0.00008958534,0.00009436205,0.00003787572],"category_scores_gemma":[0.0001378441,0.0001236938,0.00005623585,0.0003677722,0.0001274168,0.00007854928,0.0001146025,0.0001138912,0.000002009614],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002251992,"about_ca_system_score_gemma":0.00001548631,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001805645,"about_ca_topic_score_gemma":0.00002798523,"domain_scores_codex":[0.9990854,0.00002247414,0.0003230556,0.0002678946,0.0001400094,0.0001611542],"domain_scores_gemma":[0.9987131,0.0007800793,0.00007376647,0.0003109725,0.00004025193,0.00008184],"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":[0.000004300964,0.000115049,0.0005004496,0.001126055,0.00004103031,0.000003053252,0.0002868159,0.000004007818,0.00009012138,0.9864791,0.0003733776,0.01097666],"study_design_scores_gemma":[0.0001446077,0.00006408091,0.0004161188,0.0001084542,0.0000729505,0.00001939179,0.0003282426,0.2185221,0.00004844395,0.7789305,0.00115825,0.0001868233],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7999864,0.0007497815,0.1969001,0.0001967614,0.00007139434,0.0001365821,0.0001431972,0.00008556499,0.001730168],"genre_scores_gemma":[0.9909518,0.0002971754,0.008045194,0.00003231435,0.00004060058,0.00002451996,0.00002613069,0.00002123791,0.000560981],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2185181,"threshold_uncertainty_score":0.5044088,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0168883437517618,"score_gpt":0.2672958909247494,"score_spread":0.2504075471729876,"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."}}