{"id":"W3103483747","doi":"","title":"Killing tensors, warped products and the orthogonal separation of the Hamilton-Jacobi equation","year":2016,"lang":"en","type":"article","venue":"","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Constant curvature; Separable space; Mathematics; Separation of variables; Hamiltonian (control theory); Bipolar coordinates; Curvature; Pure mathematics; Mathematical analysis; Orthogonal coordinates; Hamilton–Jacobi equation; Geometry; Partial differential equation; Mathematical optimization","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":[0.0001807779,0.00005697327,0.00007659871,0.000008553176,0.00009809992,0.00001366006,0.00006203701,0.00001306015,0.00005782395],"category_scores_gemma":[0.00001159091,0.00002068787,0.00004068618,0.00005933443,0.0001008373,0.00006283472,0.00002478885,0.00003592699,0.000005467012],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000003398132,"about_ca_system_score_gemma":0.00003019629,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004805413,"about_ca_topic_score_gemma":0.000003957927,"domain_scores_codex":[0.9995415,0.00005271631,0.0001320617,0.00009999348,0.00009130951,0.00008242132],"domain_scores_gemma":[0.9995897,0.00009555314,0.00007237574,0.0001616064,0.00006669325,0.00001407744],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.00009435145,0.0001006105,0.04017556,0.00001606189,0.0001112133,7.09403e-8,0.001570617,0.0001817607,0.03139562,0.900655,0.000829374,0.02486978],"study_design_scores_gemma":[0.016207,0.0002391202,0.1456296,0.0004319766,0.0004813653,0.000006647942,0.003314001,0.1261608,0.4002579,0.228129,0.07773603,0.001406565],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9752893,0.00001996778,0.01611679,0.003519976,0.000102228,0.0002709978,0.00001908784,0.000007865958,0.00465377],"genre_scores_gemma":[0.9956854,0.000004452945,0.0004685834,0.00003569222,0.0002543544,0.0000056453,0.000004802812,0.000004641952,0.003536416],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.672526,"threshold_uncertainty_score":0.08436269,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01323987927988088,"score_gpt":0.2473744648609911,"score_spread":0.2341345855811102,"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."}}