{"id":"W2951922002","doi":"10.48550/arxiv.1201.4687","title":"Coarse structures on groups","year":2012,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Metrization theorem; Group (periodic table); Mathematics; Subspace topology; Cartesian product; Topological group; Hausdorff space; Pure mathematics; Context (archaeology); Topology (electrical circuits); Dimension (graph theory); Zero-dimensional space; Discrete group; Topological space; Locally compact space; Free product; Hausdorff dimension; Topological vector space; Discrete mathematics; Combinatorics; Mathematical analysis; Physics; Separable space","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002937499,0.0004494952,0.0004785629,0.0002680587,0.0001741891,0.00005451171,0.0009826355,0.0005310657,0.0006324587],"category_scores_gemma":[0.0002733578,0.0004641462,0.0002332215,0.0002991354,0.0001931362,0.0001866685,0.001297004,0.001588084,0.0003339776],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004107561,"about_ca_system_score_gemma":0.0001273664,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002534457,"about_ca_topic_score_gemma":0.00003494539,"domain_scores_codex":[0.9978608,0.0002350697,0.0002183416,0.0008541714,0.0002043655,0.0006271768],"domain_scores_gemma":[0.9974132,0.0004435095,0.0001997253,0.001463695,0.0001673306,0.0003125043],"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":[0.0001490479,0.0001904654,0.0009138454,0.0002473202,0.0001561936,0.0002615843,0.0002685293,0.01307234,0.00007173561,0.9828645,0.001462758,0.0003416602],"study_design_scores_gemma":[0.0006989947,0.00007194655,0.0004783977,0.0001121345,0.0001395031,0.000005881382,0.0002780168,0.006939628,0.0007535088,0.9891039,0.0007089778,0.0007090907],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9657819,0.00006315493,0.02416806,0.00003967297,0.0006203928,0.0006652609,0.00007226343,0.0002903021,0.008298961],"genre_scores_gemma":[0.9945788,0.00006880923,0.001838442,0.00006155206,0.0002704639,0.00000201119,0.00002564744,0.00008331135,0.003070928],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0287969,"threshold_uncertainty_score":0.999781,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1961080589611997,"score_gpt":0.2697922701174936,"score_spread":0.0736842111562939,"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."}}