{"id":"W2950320606","doi":"10.1215/00127094-2010-216","title":"Random walks on the mapping class group","year":2011,"lang":"en","type":"article","venue":"Duke Mathematical Journal","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":103,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Centre de Recherches Mathématiques; California Institute of Technology; National Science Foundation","keywords":"Mapping class group; Random walk; Group (periodic table); Mathematics; Class (philosophy); Combinatorics; Surface (topology); Element (criminal law); Pure mathematics; Geometry; Statistics; Computer science; Physics; Artificial intelligence","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00195047,0.0002273848,0.0004443621,0.0002021014,0.0003278903,0.00007295813,0.0005250458,0.0001379066,0.006399835],"category_scores_gemma":[0.002432359,0.0001210122,0.0002716158,0.0003075735,0.0001919856,0.00007424992,0.0000963297,0.0007807342,0.0007687038],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004462173,"about_ca_system_score_gemma":0.00002651762,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001230586,"about_ca_topic_score_gemma":6.486432e-7,"domain_scores_codex":[0.9979481,0.000248866,0.0006583247,0.0001810656,0.000471165,0.0004925552],"domain_scores_gemma":[0.9965506,0.002507092,0.0002758363,0.0003954594,0.00007156186,0.0001994202],"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":[0.00004763681,0.0003106626,0.00003906453,0.00003782976,0.00009895158,0.00007511277,0.001997757,1.362133e-7,0.0000561025,0.9862493,0.009275493,0.001811896],"study_design_scores_gemma":[0.001085074,0.0001367869,0.0002094417,0.000106708,0.0000528403,0.0008990009,0.001517262,0.00018548,0.0001639857,0.9923993,0.003072279,0.0001718213],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4012948,0.0001057872,0.2505019,0.004946175,0.0007600733,0.0006028463,0.000003807079,0.0001731598,0.3416114],"genre_scores_gemma":[0.9745016,0.00001896978,0.0225925,0.0009564511,0.0003801093,0.00002153382,4.156266e-7,0.00004250023,0.001485973],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5732067,"threshold_uncertainty_score":0.9945084,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.113506317733412,"score_gpt":0.2798542629857488,"score_spread":0.1663479452523368,"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."}}