{"id":"W2093726366","doi":"10.1093/imrn/rnp063","title":"Diophantine Conditions in Well-Posedness Theory of Coupled KdV-Type Systems: Local Theory","year":2009,"lang":"en","type":"article","venue":"International Mathematics Research Notices","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":27,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Diophantine equation; Mathematics; Type (biology); Korteweg–de Vries equation; Diophantine approximation; Characterization (materials science); Coupling (piping); Pure mathematics; Zero (linguistics); Coupling parameter; Mathematical analysis; Nonlinear system; Quantum mechanics; Physics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.005333215,0.0003066151,0.0006955933,0.0006415287,0.0001186176,0.000109967,0.001179984,0.000159224,0.0004287634],"category_scores_gemma":[0.004890636,0.0002621587,0.0001316264,0.0007367184,0.0006159758,0.0004652914,0.0002242672,0.0006428559,0.0001835358],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002212467,"about_ca_system_score_gemma":0.0001417632,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009851522,"about_ca_topic_score_gemma":0.00000715388,"domain_scores_codex":[0.9954134,0.0004764746,0.001270147,0.0004218679,0.00181138,0.0006067908],"domain_scores_gemma":[0.9879753,0.009467412,0.0004652895,0.0006910276,0.00125169,0.0001492561],"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":[0.0001876481,0.001768751,0.00001590702,0.0007561804,0.000116186,0.0000302217,0.001257328,0.001253716,0.005108204,0.9889727,0.0002261761,0.0003070439],"study_design_scores_gemma":[0.0007424265,0.0001765758,0.0000881911,0.001002775,0.0000314451,0.000012909,0.002686517,0.04487971,0.00241897,0.947649,0.00007332311,0.0002381383],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5573062,0.0005583417,0.3581547,0.001041731,0.0009367517,0.002880061,0.0001036256,0.0002962821,0.07872234],"genre_scores_gemma":[0.9855168,0.00003959593,0.01244756,0.00003504994,0.0001178783,0.00006652937,0.00002397967,0.00005524159,0.001697353],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4282106,"threshold_uncertainty_score":0.9999831,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1136907149512393,"score_gpt":0.4420207468928877,"score_spread":0.3283300319416484,"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."}}