{"id":"W4320039064","doi":"10.1016/j.cnsns.2023.107167","title":"Complete classification on center of cubic planar systems symmetric with respect to a straight line","year":2023,"lang":"en","type":"article","venue":"Communications in Nonlinear Science and Numerical Simulation","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"Western University","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Center (category theory); Singular point of a curve; Mathematics; Planar; Line (geometry); Mathematical analysis; Pure mathematics; Nilpotent; Singular solution; Combinatorics; Geometry; Computer science","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":[0.000632998,0.000104132,0.0002186058,0.0006158894,0.0002177769,0.0000485801,0.0004301861,0.0000421408,0.000002545572],"category_scores_gemma":[0.0008383211,0.00008043749,0.00002010166,0.00385469,0.0002132125,0.0001514792,0.0001018059,0.0001273199,0.00001716102],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009118614,"about_ca_system_score_gemma":0.00004868592,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003241999,"about_ca_topic_score_gemma":0.00002394844,"domain_scores_codex":[0.9985433,0.0001044388,0.0004323351,0.0002569783,0.0004719912,0.0001909165],"domain_scores_gemma":[0.99761,0.001097166,0.0001623641,0.0007638333,0.0002732891,0.0000933837],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0003968753,0.002000124,0.01627349,0.0002376284,0.0000396002,0.000003062476,0.001718529,0.2699079,0.01271011,0.658062,0.00006326738,0.03858731],"study_design_scores_gemma":[0.0003393909,0.0001950458,0.01326098,0.0001223759,0.000006140257,8.408323e-7,0.0001553715,0.9832679,0.00001987342,0.001841181,0.0006874471,0.0001034286],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7019302,0.00005952966,0.2920101,0.001521575,0.0001276592,0.001583819,0.000128529,0.0001751369,0.002463498],"genre_scores_gemma":[0.9862856,0.0000179718,0.01350927,0.00002350444,0.00002003543,0.00003812383,0.00005618007,0.0000105741,0.00003875702],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.71336,"threshold_uncertainty_score":0.3280146,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1597596089641768,"score_gpt":0.4018139067779362,"score_spread":0.2420542978137594,"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."}}