{"id":"W4299431453","doi":"10.48550/arxiv.0903.2518","title":"A remainder estimate for Weyl's law on Liouville tori","year":2009,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Remainder; Torus; Mathematics; Eigenvalues and eigenvectors; Laplace transform; Integrable system; Planar; Class (philosophy); Mathematical analysis; Pure mathematics; Physics; Geometry; Computer science; Quantum mechanics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"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":[0.001950671,0.0008705002,0.001101668,0.003346682,0.0008859434,0.001338611,0.001521539,0.0007391043,0.004532246],"category_scores_gemma":[0.01138826,0.0002931036,0.00081017,0.0007394126,0.003619981,0.003517362,0.001835468,0.001983909,0.0006856534],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001464659,"about_ca_system_score_gemma":0.0005012479,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001915237,"about_ca_topic_score_gemma":0.000689194,"domain_scores_codex":[0.9993179,0.0001630026,0.00002715788,0.00009884385,0.000277189,0.0001159209],"domain_scores_gemma":[0.9965581,0.001519003,0.0003826901,0.0003251101,0.0007051396,0.000509943],"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":[0.0001212653,0.00004421053,0.002865928,0.0001607487,0.00002722901,0.000387574,0.0004322406,0.01246197,0.008065117,0.9632345,0.002440347,0.009758959],"study_design_scores_gemma":[0.00002889091,0.0001231158,0.003965952,0.0001077779,0.00003294829,0.0004977823,0.0002737296,0.2452455,0.004835458,0.7403011,0.004515883,0.00007185049],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5689262,0.002730338,0.3795348,0.002444994,0.000405308,0.0000746919,0.0003136494,0.0005900697,0.04497993],"genre_scores_gemma":[0.9726478,0.001352723,0.01400332,0.0002253435,0.0005124166,0.00007877687,0.0002893749,0.0002118902,0.01067836],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004532246,"threshold_uncertainty_score":0.01516187,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1710544836802965,"score_gpt":0.2725707205104604,"score_spread":0.1015162368301639,"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."}}