{"id":"W2046799751","doi":"10.1016/s0393-0440(01)00017-1","title":"A geometrical approach to the problem of integrability of Hamiltonian systems by separation of variables","year":2001,"lang":"en","type":"article","venue":"Journal of Geometry and Physics","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":20,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Hamiltonian system; Separable space; Hamiltonian (control theory); Separation of variables; Hamilton–Jacobi equation; Covariant Hamiltonian field theory; Curvature; Superintegrable Hamiltonian system; Lagrangian; Moving frame; Mathematical analysis; Mathematical physics; Pure mathematics; Applied mathematics; Geometry; Partial differential equation; Mathematical optimization; Computer science; Frame (networking)","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002924415,0.001135453,0.00181894,0.002210458,0.001771323,0.003277403,0.002562419,0.002648506,0.005074073],"category_scores_gemma":[0.005363281,0.00102271,0.002514111,0.001184756,0.008267757,0.009030375,0.003683267,0.00614455,0.0003771995],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001734836,"about_ca_system_score_gemma":0.001011563,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001089118,"about_ca_topic_score_gemma":0.0009015142,"domain_scores_codex":[0.9989119,0.0006003607,0.00005238554,0.00009037972,0.0002495521,0.00009547402],"domain_scores_gemma":[0.9978756,0.001479015,0.0001593994,0.0001708744,0.0001559519,0.0001592398],"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":[0.000004303336,0.000007863172,0.00001687344,0.00001336744,0.000004816779,0.00001597443,0.00005230791,0.001863097,0.0001150077,0.9970301,0.0002183576,0.0006579108],"study_design_scores_gemma":[0.000008323491,0.000005319114,0.00002050663,0.00000462743,0.000001660727,0.00001603269,0.00001609203,0.01012997,0.00002387094,0.9893129,0.000456413,0.000004253028],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08541544,0.005039251,0.8261291,0.0144945,0.00082957,0.00008555635,0.0001602519,0.0001261269,0.06772019],"genre_scores_gemma":[0.749383,0.004501933,0.2182661,0.001744058,0.003220189,0.0002650165,0.0002447685,0.0003066203,0.02206831],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005074073,"threshold_uncertainty_score":0.01697451,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0138488082499823,"score_gpt":0.2671122150299161,"score_spread":0.2532634067799338,"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."}}