{"id":"W2906019317","doi":"10.1088/1751-8121/ab14c2","title":"On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals","year":2019,"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":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Fonds Québécois de la Recherche sur la Nature et les Technologies; Grantová Agentura České Republiky","keywords":"Quadratic growth; Integrable system; Ansatz; Quadratic equation; Invariant (physics); Euclidean geometry; Type (biology); Bounded function","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003787525,0.0002167086,0.0005332407,0.00005864161,0.00003433213,0.0001181446,0.0001356502,0.00006758983,0.0002898705],"category_scores_gemma":[0.00002444707,0.0001352883,0.00007630638,0.0001591445,0.000174786,0.0001404537,0.00004730682,0.0005506243,0.00002693368],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001679418,"about_ca_system_score_gemma":0.00007671519,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007210563,"about_ca_topic_score_gemma":3.820729e-7,"domain_scores_codex":[0.9987636,0.00007083771,0.0004258295,0.0001993738,0.0002944623,0.0002458711],"domain_scores_gemma":[0.998909,0.0005089801,0.0001300739,0.0001559646,0.0001337613,0.0001622145],"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":[0.0001952371,0.0003818159,0.000301003,0.00007804287,0.00004565045,0.00001238403,0.0002373216,0.00004698012,0.000371631,0.9970303,0.00004719698,0.001252389],"study_design_scores_gemma":[0.001034999,0.001568212,0.000106204,0.0006269495,0.00004148224,0.0000350237,0.0004745452,0.0427302,0.0003162172,0.9528599,0.00002398723,0.0001822807],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.983393,0.00004130686,0.01031779,0.0002315643,0.0000921317,0.0002192347,0.000005920504,0.000004065823,0.005695031],"genre_scores_gemma":[0.9988465,0.000007271617,0.0007593016,0.00005614964,0.0001292692,0.000007079801,0.000002316457,0.00002294762,0.0001691137],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04417045,"threshold_uncertainty_score":0.5516897,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005904220669684801,"score_gpt":0.2146606556354176,"score_spread":0.2087564349657328,"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."}}