{"id":"W2883053347","doi":"10.1112/plms.12394","title":"Random walks, WPD actions, and the Cremona group","year":2021,"lang":"en","type":"article","venue":"Proceedings of the London Mathematical Society","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Simons Foundation; Alfred P. Sloan Foundation","keywords":"Random walk; Sequence (biology); Group (periodic table); Class (philosophy); Degree (music); Random graph","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001786524,0.0002696808,0.0007426417,0.00001392805,0.0003590535,0.0001539565,0.0004693242,0.0001777253,0.0002031142],"category_scores_gemma":[0.003114458,0.0001367631,0.0007192951,0.0003375498,0.0007170129,0.0001501061,0.0005161412,0.0004462952,0.00001009053],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003860325,"about_ca_system_score_gemma":0.00002611363,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002933853,"about_ca_topic_score_gemma":0.000001043154,"domain_scores_codex":[0.9979402,0.00003090936,0.000727694,0.000318324,0.0006344728,0.0003483514],"domain_scores_gemma":[0.9965577,0.002309897,0.0003985852,0.000328544,0.0002949306,0.0001104017],"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":[0.0000511181,0.00025866,0.00005636746,0.001342586,0.0001712793,3.216084e-7,0.001349083,1.641141e-7,0.003749141,0.9886935,0.003978056,0.0003497552],"study_design_scores_gemma":[0.002383209,0.00001435706,0.0001001882,0.0002650952,0.0002788527,0.00007377287,0.001341808,0.01042989,0.00229656,0.9818408,0.0007951967,0.000180222],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8950354,0.001198609,0.0192172,0.02378449,0.0002709389,0.002631083,0.00003684515,0.0002647224,0.05756066],"genre_scores_gemma":[0.8908238,0.0006491857,0.1014914,0.0009986698,0.0002139878,0.0001891957,0.000002499988,0.0001083483,0.005522874],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08227421,"threshold_uncertainty_score":0.5577036,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02358800212735437,"score_gpt":0.2695178882197901,"score_spread":0.2459298860924357,"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."}}