{"id":"W2896674220","doi":"10.1093/qmath/hay049","title":"Metric semi-groups of normal states determine F-algebras","year":2018,"lang":"en","type":"article","venue":"The Quarterly Journal of Mathematics","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Fundamental Research Funds for the Central Universities; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China; Ministry of Science and Technology","keywords":"Mathematics; Pure mathematics; Metric (unit); Algebra over a field; Group (periodic table); Group algebra; Fourier transform; Locally compact group; Locally compact space; Mathematical analysis; Physics; Quantum mechanics","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":[0.0009348143,0.0003905908,0.0005151486,0.00128968,0.00127949,0.001782362,0.0004756641,0.0006012758,0.003015458],"category_scores_gemma":[0.00200574,0.000238368,0.0006551676,0.000338588,0.003536626,0.00297165,0.001794325,0.0008871581,0.0004944979],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007273555,"about_ca_system_score_gemma":0.0005236015,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005760553,"about_ca_topic_score_gemma":0.0003698013,"domain_scores_codex":[0.9991586,0.0001844639,0.00006780725,0.0001728104,0.0002391536,0.0001771749],"domain_scores_gemma":[0.9984212,0.0001990173,0.0002511491,0.0001554905,0.000410271,0.0005629307],"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":[0.00006600456,0.00003740731,0.001180658,0.00001564909,0.00001079833,0.0001589352,0.0005898095,0.0005234614,0.004554021,0.9872155,0.0004642064,0.005183495],"study_design_scores_gemma":[0.00003172971,0.0001343338,0.001325339,0.00001246786,0.000008855231,0.0004402171,0.0005108531,0.006243168,0.004247354,0.983487,0.003527034,0.00003158401],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9130858,0.0001471465,0.05577335,0.0003942956,0.0001484146,0.00004286989,0.00007605789,0.0001753782,0.03015672],"genre_scores_gemma":[0.9895346,0.00006254284,0.005701531,0.00006827647,0.00007876175,0.00002958087,0.00007390379,0.00002746172,0.004423275],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003015458,"threshold_uncertainty_score":0.01008773,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03554147114207044,"score_gpt":0.3348963163662402,"score_spread":0.2993548452241697,"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."}}