{"id":"W2152522190","doi":"10.4153/cmb-2005-056-2","title":"Toeplitz Algebras and Extensions of Irrational Rotation Algebras","year":2005,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Toeplitz matrix; Mathematics; Irrational number; Algebra over a field; Extension (predicate logic); Pure mathematics; Rotation (mathematics); Toeplitz operator; Atiyah–Singer index theorem; Computer science; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007955396,0.0004470043,0.0003635102,0.001097471,0.0007280241,0.001830037,0.000523939,0.0003544255,0.00602502],"category_scores_gemma":[0.00148688,0.0001626866,0.0004226249,0.0006345662,0.00185417,0.002844861,0.001174976,0.00096452,0.0007277088],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006523379,"about_ca_system_score_gemma":0.0004261059,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004159698,"about_ca_topic_score_gemma":0.0003279133,"domain_scores_codex":[0.9992773,0.000138834,0.00004949447,0.0001207533,0.000256752,0.0001569293],"domain_scores_gemma":[0.9992462,0.0001270043,0.0002151253,0.0001042195,0.0001488292,0.0001587083],"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":[0.00003017312,0.00002588362,0.0001577213,0.00001548521,0.000002812352,0.0001368837,0.000204824,0.0008608625,0.002953497,0.9914962,0.0002726665,0.003842961],"study_design_scores_gemma":[0.0000252548,0.00007268989,0.0004399085,0.00001574782,0.000005828491,0.0003466254,0.0002488652,0.008533943,0.003923002,0.9804471,0.005914453,0.00002665917],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6871367,0.0006614019,0.1799012,0.0005550781,0.0002374056,0.0001090413,0.0001799883,0.0003368958,0.1308824],"genre_scores_gemma":[0.9750367,0.0002507498,0.01349178,0.0001352731,0.0001403987,0.00004596286,0.00007137834,0.00003309804,0.01079473],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00602502,"threshold_uncertainty_score":0.02015567,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02885467811654746,"score_gpt":0.2852833877685642,"score_spread":0.2564287096520167,"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."}}