{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005363172,0.0002098816,0.0005155089,0.00004405042,0.00009286592,0.0001259537,0.0001779565,0.00005401894,0.0002360994],"category_scores_gemma":[0.00002256125,0.000150072,0.0001309324,0.0002083991,0.0004225574,0.0001871044,0.00007485655,0.0003546892,0.00003354063],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001560615,"about_ca_system_score_gemma":0.00006209547,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008920943,"about_ca_topic_score_gemma":1.661803e-7,"domain_scores_codex":[0.9985813,0.00009561917,0.0005651209,0.0001678592,0.0002575206,0.0003325121],"domain_scores_gemma":[0.9990675,0.0001863425,0.0001829372,0.0001547559,0.0002415253,0.0001668721],"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":[0.00003085897,0.0002829721,0.0003773603,0.00003807516,0.00005477258,0.000007243618,0.0003011442,0.000008675293,0.001768033,0.9958001,0.0001042323,0.001226534],"study_design_scores_gemma":[0.0005462764,0.0002644362,0.00001655085,0.0001926851,0.00003990141,0.00002952941,0.0003527468,0.04942509,0.004485189,0.9443215,0.0001467605,0.0001793711],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9389836,0.00007808996,0.05119658,0.0001865348,0.0001913323,0.0001340742,0.00001561444,0.000008116964,0.009206053],"genre_scores_gemma":[0.9968435,0.000004119508,0.001904913,0.00004056615,0.001106226,0.000004760091,0.000001909017,0.00002597875,0.00006805384],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05785987,"threshold_uncertainty_score":0.6119759,"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."}}