{"id":"W2340124329","doi":"10.1007/s00222-016-0709-x","title":"The Sine $$_\\beta $$ β operator","year":2016,"lang":"en","type":"article","venue":"Inventiones mathematicae","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Brownian motion; Random matrix; Fractional Brownian motion; Riemann zeta function; Operator (biology); Sine; Conjecture; Random walk; Affine transformation","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":[0.0005813858,0.0001393282,0.0001921491,0.00003512086,0.0003985754,0.00009784264,0.000353028,0.0000478464,0.0004146668],"category_scores_gemma":[0.0003695954,0.00006212298,0.0001474696,0.0001834571,0.0001266324,0.0001266889,0.00007279359,0.00005151739,0.0009455549],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002621857,"about_ca_system_score_gemma":0.0000217432,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001473726,"about_ca_topic_score_gemma":0.000008791173,"domain_scores_codex":[0.9988139,0.0000538723,0.000454767,0.0001808247,0.0002540291,0.0002425814],"domain_scores_gemma":[0.9977913,0.001227052,0.0001722012,0.0006314294,0.0001030139,0.00007499911],"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":[0.000006903582,0.0001012885,0.00003667009,0.00004583635,0.00003638662,7.256907e-7,0.00006336433,7.491279e-8,0.001220147,0.9745724,0.02038324,0.003532965],"study_design_scores_gemma":[0.0007032632,0.00001732805,0.00009770077,0.0001034075,0.00005080924,0.00001619892,0.00008655618,0.00005606127,0.002103366,0.9326068,0.06401464,0.0001438648],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4743715,0.001184153,0.3441243,0.08462176,0.0009947151,0.003848278,0.00008189096,0.001386357,0.08938707],"genre_scores_gemma":[0.9371914,0.0002638294,0.0186027,0.0001549543,0.0004700631,0.0007173795,0.000002934551,0.00008776464,0.04250902],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4628199,"threshold_uncertainty_score":0.9998323,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05390381332405197,"score_gpt":0.3283648351424267,"score_spread":0.2744610218183747,"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."}}