{"id":"W7140721800","doi":"10.5802/jolt.530","title":"Structure Equations of Lie Pseudo-Groups","year":2008,"lang":"en","type":"article","venue":"Journal of Lie theory","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of Minnesota; Fonds Québécois de la Recherche sur la Nature et les Technologies; National Science Foundation","keywords":"Lie theory; Simple Lie group; Infinitesimal; Adjoint representation; Adjoint representation of a Lie algebra; Lie group; Transitive relation; Cartan matrix; Lie algebra","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":[0.0001906104,0.00008170822,0.0002088212,0.00006440294,0.00008269139,0.000007985052,0.0001509914,0.0000294663,0.0007899451],"category_scores_gemma":[0.00001810313,0.00006172084,0.0001773901,0.00008076376,0.00008002477,0.0001014161,0.00002373149,0.0002180398,0.000007663885],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009636697,"about_ca_system_score_gemma":0.0001133477,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004119533,"about_ca_topic_score_gemma":3.362165e-7,"domain_scores_codex":[0.9992675,0.00006809607,0.0003364652,0.00005341965,0.0001569792,0.000117501],"domain_scores_gemma":[0.9991772,0.000164191,0.0003300899,0.0001334441,0.0001223614,0.00007270134],"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":[0.0001416143,0.0004036433,0.01159066,0.00001853025,0.0004212536,0.00002200624,0.002905633,0.0005301187,0.01631123,0.9560743,0.001828753,0.009752265],"study_design_scores_gemma":[0.001630052,0.0003678445,0.01131784,0.0001007057,0.000177681,0.00009333911,0.002339405,0.000260755,0.01881665,0.9601851,0.004407009,0.0003036405],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9826187,0.0001232737,0.01094437,0.0001190305,0.0002273963,0.00003760231,0.00005761743,0.000002976093,0.00586897],"genre_scores_gemma":[0.9962882,0.000009156906,0.001986832,0.00003560352,0.001077095,2.147439e-7,0.000004633504,0.00001060196,0.0005877079],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01366939,"threshold_uncertainty_score":0.8649344,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01311599195122821,"score_gpt":0.2518923018807804,"score_spread":0.2387763099295522,"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."}}