{"id":"W4361197154","doi":"10.1007/s00220-024-04988-7","title":"Jánossy Densities and Darboux Transformations for the Stark and Cylindrical KdV Equations","year":2024,"lang":"en","type":"article","venue":"Communications in Mathematical Physics","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University","funders":"Fundação para a Ciência e a Tecnologia; Fonds De La Recherche Scientifique - FNRS","keywords":"Korteweg–de Vries equation; Mathematics; Superposition principle; Airy function; Mathematical analysis; Mathematical physics; Differential equation; Kernel (algebra); Point (geometry); Nonlinear system; Pure mathematics; Physics; Quantum mechanics; Geometry","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":[0.0005621655,0.0001493147,0.0002314433,0.00006434494,0.0005135729,0.0002363707,0.0003945244,0.00006543475,0.00001089636],"category_scores_gemma":[0.000371104,0.0001082777,0.00008001798,0.0003653734,0.0004099343,0.0002154774,0.0001506024,0.0002784135,0.00001282539],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003270576,"about_ca_system_score_gemma":0.00004684805,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005874709,"about_ca_topic_score_gemma":0.00002660366,"domain_scores_codex":[0.9989825,0.00006744009,0.0004504707,0.0001724443,0.0001416623,0.0001854529],"domain_scores_gemma":[0.9869406,0.01199761,0.00005178907,0.0008866389,0.00006951847,0.00005384352],"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":[0.000003325092,0.0001127231,0.000004531504,0.0002571605,0.00003465476,1.106421e-7,0.002739561,0.00001264706,0.0000267513,0.9865528,0.0003726268,0.009883045],"study_design_scores_gemma":[0.0002221779,0.00001128045,0.00004123137,0.00008842987,0.0001154085,0.000005031989,0.0008236124,0.2511161,0.00001266094,0.7443535,0.003109881,0.0001007336],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.008632503,0.003311074,0.9675139,0.01359742,0.00004023513,0.001640165,0.0001016761,0.0001678018,0.004995285],"genre_scores_gemma":[0.9367825,0.001011897,0.06085888,0.00007804831,0.00006361146,0.001018106,0.00002339856,0.00003255052,0.0001310019],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.92815,"threshold_uncertainty_score":0.4415437,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1208767021512096,"score_gpt":0.3927126900280314,"score_spread":0.2718359878768218,"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."}}