{"id":"W1885231901","doi":"10.1090/proc/13189","title":"Projectively universal countable metrizable groups","year":2016,"lang":"en","type":"preprint","venue":"Proceedings of the American Mathematical Society","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"Natural Sciences and Engineering Research Council of Canada; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior","keywords":"Metrization theorem; Countable set; Mathematics; Quotient; Group (periodic table); Topological group; Quotient group; Pure mathematics; Combinatorics; Discrete mathematics; Topology (electrical circuits); Cyclic group; Separable space; Physics; Mathematical analysis","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008130977,0.0008500678,0.0005102608,0.001134121,0.001666202,0.002387257,0.0007876217,0.0005437199,0.01551202],"category_scores_gemma":[0.002814396,0.0003547379,0.001144653,0.0006042743,0.003297941,0.004471788,0.004493162,0.002037497,0.00210286],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001474224,"about_ca_system_score_gemma":0.0006509334,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001263653,"about_ca_topic_score_gemma":0.001156893,"domain_scores_codex":[0.9987751,0.000259857,0.0000570589,0.0003630863,0.0003110624,0.0002338531],"domain_scores_gemma":[0.9983007,0.0005247383,0.0002449274,0.0003137551,0.0003032024,0.0003127167],"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":[0.00003228225,0.00001441916,0.0002481033,0.00003552917,0.00001055468,0.00009416059,0.0003897726,0.0004274322,0.001089088,0.99359,0.001099681,0.00296896],"study_design_scores_gemma":[0.00004906639,0.00009670194,0.0008801811,0.00002988581,0.00003435581,0.0002923543,0.0005674263,0.006302633,0.005105724,0.9620763,0.02453487,0.00003047828],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4603844,0.0008306504,0.2737961,0.004329594,0.000439639,0.0001145335,0.0010257,0.001788765,0.2572906],"genre_scores_gemma":[0.9476541,0.0002824742,0.01920476,0.0003337947,0.0002485302,0.00009390613,0.0007309885,0.0001999388,0.03125159],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01551202,"threshold_uncertainty_score":0.05189288,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02659842870677681,"score_gpt":0.3029231952107271,"score_spread":0.2763247665039503,"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."}}