{"id":"W1997427749","doi":"10.1007/s11005-012-0593-2","title":"Weyl’s Law and Connes’ Trace Theorem for Noncommutative Two Tori","year":2012,"lang":"en","type":"article","venue":"Letters in Mathematical Physics","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University; Western University","funders":"","keywords":"Noncommutative geometry; TRACE (psycholinguistics); Laplace operator; Torus; Invariant (physics); Conformal map; Eigenvalues and eigenvectors; Noncommutative quantum field theory","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":[],"consensus_categories":[],"category_scores_codex":[0.0007317801,0.000253785,0.00048283,0.00003318039,0.0001083977,0.00004503988,0.0002392116,0.00005675715,0.00004082028],"category_scores_gemma":[0.0003714335,0.0002133211,0.00008691849,0.0001574895,0.0003172124,0.0004330371,0.0001243742,0.0003607776,0.00004814388],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001727067,"about_ca_system_score_gemma":0.00001875867,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001176189,"about_ca_topic_score_gemma":0.00001497355,"domain_scores_codex":[0.9982505,0.0001467717,0.0003802925,0.0002433938,0.0003196851,0.0006593848],"domain_scores_gemma":[0.995401,0.003903137,0.00008950014,0.0003959577,0.00005102413,0.0001594014],"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":[0.00002761634,0.0002454153,0.000156883,0.0003194988,0.00002970523,0.000002998101,0.003541709,0.00001100426,0.003062261,0.9914055,0.0002452959,0.0009520397],"study_design_scores_gemma":[0.001060579,0.00003779901,0.00001640957,0.00009594657,0.00002747398,0.000007845469,0.0007354206,0.002301538,0.007237752,0.9880679,0.0001393178,0.0002720382],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4595068,0.00008622367,0.5319258,0.001595663,0.0001265673,0.001396282,0.00002561556,0.00008950469,0.00524754],"genre_scores_gemma":[0.8435687,0.00000235584,0.1545485,0.001263456,0.0003031059,0.0002096566,0.000002869065,0.00007073944,0.00003061942],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.3840618,"threshold_uncertainty_score":0.869898,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05644598164182991,"score_gpt":0.3873709072082874,"score_spread":0.3309249255664575,"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."}}