{"id":"W2975396334","doi":"10.3842/sigma.2019.091","title":"Locally Nilpotent Derivations of Free Algebra of Rank Two","year":2019,"lang":"en","type":"article","venue":"Symmetry Integrability and Geometry Methods and Applications","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Fundação de Amparo à Pesquisa do Estado de São Paulo; Centre de Recherches Mathématiques","keywords":"Mathematics; Kernel (algebra); Rank (graph theory); Multiplicative function; Nilpotent; Cellular algebra; Pure mathematics; Symmetric algebra; Algebra over a field; Associative property; Division algebra; Locally nilpotent; Polynomial; Universal enveloping algebra; Commutative property; Filtered algebra; Algebra representation; Nilpotent group; Combinatorics; Mathematical analysis","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":[0.001103281,0.0001668185,0.0005289355,0.0001888537,0.00008903698,0.00001704767,0.0002004618,0.0001117303,0.0001376604],"category_scores_gemma":[0.001113308,0.0001341997,0.0001201848,0.0007311779,0.0002724782,0.00009922426,0.0001405209,0.0001804297,0.000002279969],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002051199,"about_ca_system_score_gemma":0.00002723717,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001370115,"about_ca_topic_score_gemma":0.00001791048,"domain_scores_codex":[0.9983662,0.0002090465,0.0007255647,0.0003560216,0.0001815474,0.0001615601],"domain_scores_gemma":[0.9963659,0.002209597,0.0002991727,0.0007482711,0.0002737209,0.0001033208],"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":[0.00001585504,0.0002693713,0.0050668,0.0004723654,0.00005818465,2.366303e-8,0.0000826262,0.000006651058,0.009828619,0.8867433,0.00001028198,0.09744592],"study_design_scores_gemma":[0.0006331269,0.00009837009,0.004676839,0.00006576017,0.00008118795,0.000003280275,0.0005880949,0.002941046,0.004505715,0.9856831,0.0005546836,0.0001687494],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2738385,0.0002242581,0.7239088,0.0001099794,0.00003484585,0.0006299658,0.00008180873,0.00002264501,0.0011492],"genre_scores_gemma":[0.6631038,0.00003686,0.3366135,0.00001457942,0.00001907325,0.00008202093,0.00001123951,0.00001004621,0.0001088793],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.3892654,"threshold_uncertainty_score":0.5472507,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02755169772849688,"score_gpt":0.3676080420569637,"score_spread":0.3400563443284668,"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."}}