{"id":"W2111018658","doi":"10.3842/sigma.2011.036","title":"Models of Quadratic Algebras Generated by Superintegrable Systems in 2D","year":2011,"lang":"en","type":"article","venue":"Symmetry Integrability and Geometry Methods and Applications","topic":"Quantum Mechanics and Non-Hermitian Physics","field":"Physics and Astronomy","cited_by":30,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal; Université du Québec à Montréal","funders":"Université de Montréal; Centre de Recherches Mathématiques","keywords":"Eigenvalues and eigenvectors; Quadratic equation; Degenerate energy levels; Mathematics; Realization (probability); Pure mathematics; Quantization (signal processing); Hamiltonian (control theory); Set (abstract data type); Algebra over a field; Applied mathematics; Mathematical analysis; Physics; Quantum mechanics; Computer science; Mathematical optimization; Geometry; Algorithm","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001102811,0.0002394033,0.0004941106,0.0001637008,0.0001090552,0.00004060904,0.000176079,0.0001030327,0.0001098495],"category_scores_gemma":[0.00001909319,0.0002089426,0.00008413786,0.0008177704,0.0001711795,0.0001796247,0.00006942167,0.0002955968,0.000003148063],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001744563,"about_ca_system_score_gemma":0.0000412105,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002336879,"about_ca_topic_score_gemma":0.000007833585,"domain_scores_codex":[0.998328,0.0002634664,0.0005541009,0.0004767739,0.000108279,0.0002693564],"domain_scores_gemma":[0.9989007,0.0002657561,0.0001438808,0.000423233,0.0001225237,0.0001439513],"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":[0.000014094,0.0004648057,0.006147572,0.0001249364,0.00006332234,1.225432e-7,0.0003123695,0.000007690277,0.006591898,0.9197066,0.00005209377,0.06651449],"study_design_scores_gemma":[0.0005322584,0.0001493333,0.0009151893,0.00007313289,0.00007966059,0.000002800972,0.003751994,0.03381431,0.03101131,0.9278678,0.001313238,0.0004889959],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.446343,0.001200618,0.5476044,0.00002290458,0.00005526883,0.0005634497,0.0002134918,0.00002098631,0.003975858],"genre_scores_gemma":[0.9753935,0.00007271833,0.02402927,0.00001708456,0.00003849236,0.0002745937,0.00004641789,0.00001944456,0.0001085199],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5290504,"threshold_uncertainty_score":0.8520433,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03370084986263237,"score_gpt":0.3066235442080378,"score_spread":0.2729226943454054,"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."}}