{"id":"W2932664307","doi":"10.1063/1.5099239","title":"Rationally weighted Hurwitz numbers, Meijer <i>G</i>-functions and matrix integrals","year":2019,"lang":"en","type":"article","venue":"Journal of Mathematical Physics","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal; Concordia University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Grassmannian; TRACE (psycholinguistics); Hypergeometric function; Hurwitz matrix; Hypergeometric distribution; Matrix (chemical analysis); Basis (linear algebra); Appell series; Generating function; Mellin transform","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0009593052,0.0002754764,0.000825914,0.0001007497,0.00009824989,0.0001093244,0.0002246303,0.0001394088,0.002178937],"category_scores_gemma":[0.000615493,0.0001918447,0.0003255346,0.0002490319,0.000102219,0.0003955079,0.00007596048,0.0004449222,0.0004959168],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005516003,"about_ca_system_score_gemma":0.0001033072,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001243221,"about_ca_topic_score_gemma":7.356686e-7,"domain_scores_codex":[0.9976514,0.0001135959,0.001145353,0.000188377,0.000622433,0.0002788258],"domain_scores_gemma":[0.9962459,0.002136597,0.0006433648,0.0003675643,0.0003805344,0.0002260029],"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":[0.00006012543,0.0005593018,0.0001086982,0.0004564795,0.000225244,0.0000058537,0.0003550712,0.000006326838,0.001428131,0.9705204,0.02535223,0.0009221482],"study_design_scores_gemma":[0.0008255537,0.0002113445,0.00002447459,0.0003077608,0.0002432617,0.0002209182,0.0004565438,0.001100865,0.0006574668,0.9919872,0.003723664,0.0002409615],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7422445,0.0001926661,0.1966747,0.001834022,0.0008576966,0.0008511127,0.00003530129,0.00009969264,0.05721025],"genre_scores_gemma":[0.7413738,0.00008037373,0.2184361,0.0004613959,0.001786537,0.00002930745,0.00001080647,0.0001771503,0.03764456],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02176134,"threshold_uncertainty_score":0.9987332,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02463147467022128,"score_gpt":0.3037574120240979,"score_spread":0.2791259373538766,"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."}}