{"id":"W2808710410","doi":"10.1088/1751-8121/aadc23","title":"General <i>N</i> th-order superintegrable systems separating in polar coordinates","year":2018,"lang":"en","type":"article","venue":"Journal of Physics A Mathematical and Theoretical","topic":"Quantum Mechanics and Non-Hermitian Physics","field":"Physics and Astronomy","cited_by":22,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Superintegrable Hamiltonian system; Polar coordinate system; Hamiltonian (control theory); Euclidean geometry; Hamiltonian system; Separation of variables; Mathematics; Conjecture; Mathematical physics; Generalized coordinates; Polar; Integrable system; Polynomial; Order (exchange); Pure mathematics; Mathematical analysis; Physics; Covariant Hamiltonian field theory; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004168875,0.0003577643,0.0006216363,0.0008194892,0.0009302789,0.001869882,0.0008715761,0.0006996142,0.003570487],"category_scores_gemma":[0.0006921774,0.0002908117,0.0004634104,0.0004764166,0.001994229,0.001323648,0.0008656078,0.0007790137,0.000287102],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005823658,"about_ca_system_score_gemma":0.0003813563,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006541932,"about_ca_topic_score_gemma":0.0006894187,"domain_scores_codex":[0.9997632,0.00005395107,0.00001362924,0.00002755477,0.00007212074,0.00006957526],"domain_scores_gemma":[0.9996152,0.00008436511,0.0000802228,0.00004866636,0.00006885976,0.0001026905],"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":[0.00004925582,0.00002832865,0.000697389,0.00005361226,0.00001943821,0.0008245499,0.0001798342,0.01499914,0.007697306,0.973228,0.0004897719,0.001733455],"study_design_scores_gemma":[0.00006019121,0.0001148758,0.001621381,0.00003306911,0.00002163592,0.001530638,0.0004553191,0.3072327,0.003956593,0.6813999,0.003520306,0.00005340315],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8522449,0.0006837299,0.09171473,0.0005413275,0.0001107197,0.00004986811,0.0001071185,0.0001155867,0.054432],"genre_scores_gemma":[0.9903136,0.0001764233,0.005132015,0.00004851386,0.00003957959,0.00002172617,0.00005164629,0.00002407343,0.00419243],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003570487,"threshold_uncertainty_score":0.01194447,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008128516910982842,"score_gpt":0.249668081401927,"score_spread":0.2415395644909442,"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."}}