{"id":"W1532469721","doi":"10.48550/arxiv.0804.3764","title":"Conditions implying the uniqueness of the weak$^*$-topology on certain group algebras","year":2008,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Multiplication (music); Mathematics; Uniqueness; Dual (grammatical number); Separable space; Pure mathematics; Group (periodic table); Algebra over a field; Locally compact space; Locally compact group; Topology (electrical circuits); Discrete mathematics; Combinatorics; Mathematical analysis; Physics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003772028,0.0003696703,0.0004846679,0.0002060223,0.0006117971,0.00002295116,0.001828421,0.0003867547,0.0001472687],"category_scores_gemma":[0.0004090073,0.0002645894,0.0003651492,0.0006427398,0.001043408,0.00009895286,0.001625994,0.001441287,0.00003099829],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003449536,"about_ca_system_score_gemma":0.0003124935,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002038848,"about_ca_topic_score_gemma":0.0002425669,"domain_scores_codex":[0.9975159,0.0007727369,0.0003348227,0.0006940798,0.0002066434,0.0004758306],"domain_scores_gemma":[0.9959248,0.00139869,0.0003852193,0.001933396,0.0002519762,0.0001059115],"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":[0.00006256797,0.0001838873,0.001730733,0.0001272465,0.0001821292,0.00007949778,0.000397899,0.02118856,0.000397081,0.9747728,0.0008422661,0.00003534046],"study_design_scores_gemma":[0.0008884449,0.0001272068,0.002981946,0.0002983671,0.0002011786,0.00003764374,0.001627608,0.007373111,0.002784834,0.9822983,0.0007973892,0.0005839384],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9818668,0.0000294393,0.01118782,0.0004962262,0.0003593948,0.00112344,0.0001066766,0.0001049882,0.004725208],"genre_scores_gemma":[0.9976482,0.0002253993,0.0001816567,0.0001254603,0.00006697252,0.00000977375,0.00001767951,0.0000570082,0.00166787],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01578137,"threshold_uncertainty_score":0.9999806,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1436900712001534,"score_gpt":0.2788665354329127,"score_spread":0.1351764642327593,"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."}}