{"id":"W3101379558","doi":"","title":"Moment determinants as isomonodromic tau functions","year":2013,"lang":"en","type":"article","venue":"","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"","keywords":"Toeplitz matrix; Mathematics; Ramanujan tau function; Orthogonality; Random matrix; Partition (number theory); Orthogonal polynomials; Pure mathematics; Class (philosophy); Semiclassical physics; Matrix (chemical analysis); Moment (physics); Ramanujan's sum; Combinatorics; Eigenvalues and eigenvectors","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":["insufficient_payload"],"category_scores_codex":[0.0000429903,0.0001046131,0.0001328101,0.00006766601,0.00008084763,0.00002537196,0.00009249616,0.00004606264,0.008051115],"category_scores_gemma":[0.00005040941,0.00008095243,0.00005363264,0.00009832799,0.00002228748,0.000180652,0.00005070592,0.00006991226,0.009440764],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003064037,"about_ca_system_score_gemma":0.00001327129,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000213111,"about_ca_topic_score_gemma":0.00001347646,"domain_scores_codex":[0.9993325,0.000009871685,0.0001784762,0.0001544679,0.0001099276,0.0002147898],"domain_scores_gemma":[0.9994632,0.00009226467,0.00004721493,0.0002744267,0.00003777449,0.00008514792],"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":[0.00002708398,0.001454696,0.01501271,0.000229092,0.0002167084,0.00004317271,0.001088559,0.00002434374,0.01602934,0.4047511,0.3063499,0.2547733],"study_design_scores_gemma":[0.0004505985,0.0001252131,0.003057303,0.00001760689,0.00002649877,0.00003902309,0.0007157649,0.000342028,0.009324124,0.9790679,0.00653992,0.0002939822],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9584424,0.00001748633,0.01789623,0.0002295614,0.0001619364,0.0002361222,0.000001653313,0.0001316132,0.02288302],"genre_scores_gemma":[0.9151365,0.000005927008,0.005900827,0.0002261862,0.00005895873,0.00006835066,0.000001459058,0.00001856634,0.07858328],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5743169,"threshold_uncertainty_score":0.9928557,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02418480575126904,"score_gpt":0.3057164860631436,"score_spread":0.2815316803118746,"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."}}