{"id":"W1973152599","doi":"10.1007/s00220-003-0817-5","title":"A Small-Scale Density of States Formula","year":2003,"lang":"en","type":"article","venue":"Communications in Mathematical Physics","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"","keywords":"Mathematics; Pointwise; Integrable system; Hamiltonian (control theory); Pure mathematics; Mathematical physics; Degenerate energy levels; Hamiltonian system; Quantum; Quantization (signal processing); Mathematical analysis; Quantum mechanics; Physics","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":[0.0002276997,0.00009865314,0.0002572262,0.00002004516,0.0000651365,0.00001331827,0.0003747385,0.00002742363,0.00005585967],"category_scores_gemma":[0.0000203864,0.00008729196,0.00008874026,0.0002016607,0.0001446484,0.000053934,0.0001192441,0.0001557696,0.00003974642],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001725405,"about_ca_system_score_gemma":0.00002335121,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004918559,"about_ca_topic_score_gemma":0.00001120318,"domain_scores_codex":[0.9991829,0.0001079871,0.0003620648,0.0001021844,0.00008975556,0.0001551235],"domain_scores_gemma":[0.9984346,0.0003436959,0.0001066167,0.001006062,0.00006201223,0.00004702212],"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":[0.000001243355,0.0005805347,0.01044191,0.00003670116,0.00001350323,4.851092e-8,0.0004492191,0.00006325712,0.0002382198,0.9870407,0.00001652939,0.001118122],"study_design_scores_gemma":[0.0002187088,0.00001229562,0.0004332529,0.00006858816,0.00001235689,3.032119e-7,0.0004814013,0.02979478,0.001166833,0.9674625,0.0002426236,0.0001062891],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5393805,0.00005481176,0.3934438,0.0001083612,0.00002631198,0.0003348713,0.00002217274,0.00002487803,0.06660434],"genre_scores_gemma":[0.9796751,0.00000481769,0.02015433,0.000009869839,0.00001218521,0.0000343869,0.00002075171,0.00001119223,0.00007742495],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4402946,"threshold_uncertainty_score":0.3559663,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04242100910858519,"score_gpt":0.2899523171161481,"score_spread":0.2475313080075629,"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."}}