{"id":"W2049851780","doi":"10.1007/s00039-008-0670-y","title":"Fine Properties of the Integrated Density of States and a Quantitative Separation Property of the Dirichlet Eigenvalues","year":2008,"lang":"en","type":"article","venue":"Geometric and Functional Analysis","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":104,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Omega; Combinatorics; Mathematics; Dirichlet boundary condition; Dirichlet distribution; Eigenvalues and eigenvectors; Boundary (topology); Physics; Mathematical analysis; Boundary value problem; 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":[],"consensus_categories":[],"category_scores_codex":[0.0003093795,0.00009753211,0.0003397635,0.0002222303,0.00009462431,0.000005067832,0.00007540621,0.00003242854,0.00003452505],"category_scores_gemma":[0.00105885,0.00003779215,0.000163506,0.003095274,0.0004840268,0.00005477504,0.00006957498,0.00008347294,7.301234e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001435144,"about_ca_system_score_gemma":0.00003682154,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001248999,"about_ca_topic_score_gemma":0.00003570595,"domain_scores_codex":[0.9990489,0.0001008394,0.0003325278,0.0001249168,0.0003218837,0.00007089569],"domain_scores_gemma":[0.9988358,0.0004204785,0.0002326116,0.0001731883,0.0003171864,0.00002071741],"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":[0.001240833,0.002859643,0.3554927,0.003667907,0.01722761,0.000002260361,0.01776827,0.005919091,0.1181337,0.4720324,0.003101401,0.002554168],"study_design_scores_gemma":[0.0004337881,0.0002936969,0.2433292,0.0001967981,0.004167087,0.00001381174,0.001701562,0.03016699,0.1228961,0.5964974,0.00003464966,0.0002689816],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9935615,0.0003946306,0.005632649,0.0001049929,0.0000202924,0.000146248,0.00002370823,0.000007086636,0.0001088628],"genre_scores_gemma":[0.9986423,0.00005535109,0.0007859677,0.000008663494,0.00000772253,0.000005045523,0.00000265585,0.000004911929,0.0004874008],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.124465,"threshold_uncertainty_score":0.1783417,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06920975344311536,"score_gpt":0.2766192709463373,"score_spread":0.207409517503222,"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."}}