{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003092259,0.000917518,0.001093004,0.002615994,0.001566592,0.002590159,0.001510805,0.001395092,0.01623284],"category_scores_gemma":[0.001856591,0.000466036,0.0009583397,0.001602276,0.001747372,0.002091618,0.001807386,0.00198654,0.00255022],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001087648,"about_ca_system_score_gemma":0.001072545,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002169957,"about_ca_topic_score_gemma":0.001399238,"domain_scores_codex":[0.9995593,0.0000463982,0.00002666481,0.00008435293,0.0001746379,0.0001085391],"domain_scores_gemma":[0.9987112,0.0002847832,0.0002656996,0.0001595105,0.0003657937,0.0002130124],"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":[0.0001054738,0.00004171051,0.0007186217,0.0002251789,0.00001767285,0.0001423476,0.0002947251,0.004130158,0.003009526,0.9453351,0.01713523,0.02884426],"study_design_scores_gemma":[0.00006209753,0.00009291394,0.001563531,0.00006297391,0.00002116735,0.0004630959,0.0002326956,0.03349907,0.001958841,0.9351544,0.02683463,0.00005470491],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.580503,0.003498753,0.2030079,0.00219369,0.001214803,0.0003263615,0.003763119,0.001230704,0.2042615],"genre_scores_gemma":[0.9139716,0.002028526,0.03172847,0.00074232,0.001191108,0.0001942371,0.005126568,0.0005304262,0.04448672],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01623284,"threshold_uncertainty_score":0.0543043,"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."}}