{"id":"W1992262303","doi":"10.1090/s0002-9939-2014-12217-9","title":"Commutators of small rank and reducibility of operator semigroups","year":2014,"lang":"en","type":"preprint","venue":"Proceedings of the American Mathematical Society","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Rank (graph theory); Abelian group; Semigroup; Mathematics; Unitary state; Operator (biology); Group (periodic table); Pure mathematics; Rank of an abelian group; Combinatorics; Discrete mathematics; Elementary abelian group; Physics; Chemistry; Political science; Law","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":[0.002169605,0.0004530222,0.0007401038,0.001109316,0.001418821,0.00258805,0.0007452118,0.0007813892,0.007961611],"category_scores_gemma":[0.009390811,0.0005326137,0.0009254655,0.0004132921,0.003805588,0.003304922,0.002136782,0.001437296,0.0009381066],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005091313,"about_ca_system_score_gemma":0.0005163926,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003267094,"about_ca_topic_score_gemma":0.0003004393,"domain_scores_codex":[0.9971445,0.0007942012,0.0002589708,0.0006811143,0.000671771,0.0004493897],"domain_scores_gemma":[0.991421,0.004726094,0.0008126135,0.001524686,0.0006038523,0.0009117336],"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":[0.0001323494,0.00005188867,0.0008614581,0.00004541037,0.00001096423,0.0003328735,0.001240314,0.0009206521,0.00435913,0.9874784,0.000842227,0.003724327],"study_design_scores_gemma":[0.00006359516,0.00007776957,0.000478757,0.00001223764,0.00001348976,0.00038624,0.0002318684,0.009407109,0.003353375,0.9831297,0.002818309,0.00002755164],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"other","genre_scores_codex":[0.8495497,0.0003021797,0.0958866,0.0009292695,0.0001503884,0.00008918541,0.0002600343,0.0004835431,0.05234917],"genre_scores_gemma":[0.9777233,0.00009577173,0.01412662,0.0001392286,0.0002058083,0.00009765434,0.0001861965,0.00006338377,0.007362017],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.007961611,"threshold_uncertainty_score":0.02663422,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01314740491351521,"score_gpt":0.2475386899961559,"score_spread":0.2343912850826407,"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."}}