{"id":"W2397490062","doi":"10.1515/crelle-2017-0014","title":"Splitting theorems for Poisson and related structures","year":2017,"lang":"en","type":"preprint","venue":"Journal für die reine und angewandte Mathematik (Crelles Journal)","topic":"Homotopy and Cohomology in Algebraic Topology","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Conselho Nacional de Desenvolvimento Científico e Tecnológico","keywords":"Poisson distribution; Symplectic geometry; Manifold (fluid mechanics); Mathematics; Poisson manifold; Equivariant map; Pure mathematics; Product (mathematics); Dirac (video compression format); Point (geometry); Poisson algebra; Poisson bracket; Geometry; Lie algebra; Physics; Quantum mechanics","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":["metaepi_narrow","sts","scholarly_communication","research_integrity"],"consensus_categories":["research_integrity"],"category_scores_codex":[0.004884377,0.001101846,0.002256877,0.0006147978,0.00258445,0.00134798,0.001588444,0.001513858,0.000399262],"category_scores_gemma":[0.004532075,0.0008197445,0.001127785,0.00007749192,0.0006547423,0.0003221802,0.0009599572,0.004931988,0.0000118092],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000245216,"about_ca_system_score_gemma":0.0004220148,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009678001,"about_ca_topic_score_gemma":0.00001512274,"domain_scores_codex":[0.9943801,0.0005965246,0.002402405,0.0007753168,0.0006973663,0.001148291],"domain_scores_gemma":[0.9903125,0.00203566,0.005257997,0.001157633,0.0006026569,0.0006335413],"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":[0.001002351,0.0007339527,0.0003224484,0.005120251,0.01070832,0.004260017,0.01617244,0.0001210058,0.001886873,0.8640216,0.0216702,0.07398055],"study_design_scores_gemma":[0.002115452,0.0003780091,0.00004568132,0.002029105,0.001398927,0.01769494,0.000685389,0.000343421,0.001321964,0.965868,0.007280155,0.0008389771],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7792593,0.1144824,0.04376693,0.02126228,0.01228179,0.003591604,0.0002560527,0.0004750948,0.02462462],"genre_scores_gemma":[0.8199025,0.04589732,0.1044772,0.0004297733,0.008687614,0.0001371136,0.00006614143,0.0008441936,0.01955807],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1018464,"threshold_uncertainty_score":0.9997824,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04397376167006493,"score_gpt":0.3677634423266133,"score_spread":0.3237896806565484,"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."}}