{"id":"W2913540897","doi":"10.1093/imrn/rnaa042","title":"Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds","year":2020,"lang":"en","type":"preprint","venue":"International Mathematics Research Notices","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Monochromatic color; Mathematics; Manifold (fluid mechanics); Riemannian manifold; Dimension (graph theory); Scale (ratio); Function (biology); Point (geometry); Order (exchange); Mathematical analysis; Pure mathematics; Physics; Geometry; Quantum mechanics; Optics","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":[0.001757132,0.0006588149,0.0007567696,0.0008973266,0.0007931065,0.001034188,0.001160617,0.0008986215,0.002985011],"category_scores_gemma":[0.007476075,0.0003787706,0.0006485209,0.000333714,0.002349929,0.002295504,0.0024111,0.001592704,0.0002733394],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001032527,"about_ca_system_score_gemma":0.000316529,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006856714,"about_ca_topic_score_gemma":0.000291858,"domain_scores_codex":[0.9990055,0.000186705,0.00004220682,0.000272772,0.0003484843,0.0001444648],"domain_scores_gemma":[0.9957136,0.001886881,0.0009086692,0.0005686998,0.0004954156,0.0004268131],"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":[0.0004078618,0.0001162919,0.003720088,0.0001698095,0.00006969785,0.0008853031,0.0006504449,0.1378021,0.100285,0.7408242,0.001042682,0.01402648],"study_design_scores_gemma":[0.00003914408,0.0001994269,0.003079541,0.00002712016,0.00002179415,0.0003607131,0.0001414909,0.7689695,0.02712709,0.1986627,0.001317782,0.00005369592],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6321746,0.0004963999,0.3579116,0.0005727378,0.00006988483,0.00004486979,0.00007377326,0.0001914164,0.008464848],"genre_scores_gemma":[0.9825144,0.0002244006,0.01464602,0.0001283415,0.00004323823,0.00006231016,0.00005640748,0.00009700143,0.002227847],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002985011,"threshold_uncertainty_score":0.009985805,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.3201934203221463,"score_gpt":0.4893785023910528,"score_spread":0.1691850820689065,"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."}}