{"id":"W2804745640","doi":"10.1063/1.5038658","title":"Some multidimensional integrals in number theory and connections with the Painlevé V equation","year":2018,"lang":"en","type":"article","venue":"Journal of Mathematical Physics","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Divisor (algebraic geometry); Piecewise; Polynomial; Inverse; Fourier transform; Orthogonal polynomials; Neighbourhood (mathematics); Fourier analysis","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":[0.003403638,0.0001402461,0.0003389133,0.00005117174,0.0001143861,0.00003707326,0.0001691252,0.00005482989,0.0005434852],"category_scores_gemma":[0.00214116,0.00007229661,0.00008252558,0.0002157616,0.0005449135,0.0002522895,0.00006631471,0.0004306916,0.00008110808],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000577906,"about_ca_system_score_gemma":0.00008342612,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001189618,"about_ca_topic_score_gemma":0.000003813261,"domain_scores_codex":[0.9982415,0.0004617051,0.0004387423,0.0001115053,0.0005316618,0.0002149051],"domain_scores_gemma":[0.9913372,0.007713624,0.0002928022,0.0002154942,0.0003491887,0.00009166192],"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":[0.0001622004,0.0002704568,0.00008938151,0.00004783768,0.00009103608,0.000009558295,0.001425373,0.000003587081,0.0001208658,0.9947657,0.002436886,0.0005771235],"study_design_scores_gemma":[0.000552833,0.0001574223,0.00008575095,0.0002509418,0.00006531808,0.0001469641,0.001552457,0.002169427,0.000441205,0.9943638,0.0001200983,0.00009381794],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8003799,0.00003257261,0.1944013,0.00189782,0.00006011428,0.0003388199,0.000009194508,0.00001949862,0.002860809],"genre_scores_gemma":[0.9811201,0.000006565132,0.01742086,0.0001802978,0.0005644475,0.000009032405,7.613625e-7,0.00003171267,0.0006661866],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1807402,"threshold_uncertainty_score":0.5950782,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06396432600680566,"score_gpt":0.3586819841959733,"score_spread":0.2947176581891676,"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."}}