{"id":"W2156429018","doi":"10.4171/jst/36","title":"An estimate on the number of eigenvalues of a quasiperiodic Jacobi matrix of size $n$ contained in an interval of size $n^{–C}$","year":2013,"lang":"en","type":"article","venue":"Journal of Spectral Theory","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Quasiperiodic function; Eigenvalues and eigenvectors; Mathematics; Interval (graph theory); Matrix (chemical analysis); Combinatorics; Pure mathematics; Mathematical analysis; Physics; Materials science; Quantum mechanics","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.003263482,0.0003251478,0.001391203,0.0001344957,0.00003190499,0.00002300579,0.0009579406,0.0001368583,0.001871355],"category_scores_gemma":[0.002166636,0.000209835,0.000491562,0.000324923,0.0006711408,0.0004198393,0.00005864652,0.0005111383,0.00001122478],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008985888,"about_ca_system_score_gemma":0.0001122128,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002666241,"about_ca_topic_score_gemma":0.000005619194,"domain_scores_codex":[0.9957672,0.0008351774,0.002169691,0.0001829949,0.000700742,0.0003441872],"domain_scores_gemma":[0.9911443,0.005383374,0.002173229,0.0007223454,0.0004395303,0.0001372334],"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":[0.001192633,0.002039988,0.001099994,0.0004483487,0.0001961114,0.00001014974,0.004827447,0.00005473274,0.1445926,0.8451681,0.00002811088,0.0003418275],"study_design_scores_gemma":[0.0009736134,0.001525841,0.004342825,0.0006350912,0.0001167849,0.0000311707,0.004381343,0.000287741,0.1397847,0.8477576,6.828159e-7,0.0001625463],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9966391,0.000063136,0.0005011733,0.0001572575,0.0001095527,0.0004465345,0.00001859607,0.00001434987,0.002050248],"genre_scores_gemma":[0.9820308,0.00002387479,0.01766927,0.0000317015,0.0001390769,0.000006439169,3.577752e-7,0.00005360892,0.00004483508],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0171681,"threshold_uncertainty_score":0.9990411,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02768888793909532,"score_gpt":0.3673716105579136,"score_spread":0.3396827226188183,"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."}}