{"id":"W2048549493","doi":"10.1016/j.geomphys.2012.10.004","title":"Compatible quadratic Poisson brackets related to a family of elliptic curves","year":2012,"lang":"en","type":"article","venue":"Journal of Geometry and Physics","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"Brock University","funders":"","keywords":"Mathematics; Poisson bracket; Poisson distribution; Poisson algebra; Quadratic equation; Elliptic curve; Pure mathematics; Poisson manifold; Supersingular elliptic curve; Casimir effect; Pairwise comparison; Algebra over a field; Geometry; Physics","routes":{"ca_aff":true,"ca_fund":false,"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":[0.001085283,0.001180256,0.001298869,0.003341338,0.002967221,0.002660922,0.001316335,0.001755403,0.004737433],"category_scores_gemma":[0.001945968,0.0006824145,0.0009708854,0.002161574,0.002852913,0.003634133,0.002154864,0.00203603,0.0005520959],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00185943,"about_ca_system_score_gemma":0.0006841749,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009490634,"about_ca_topic_score_gemma":0.0007264924,"domain_scores_codex":[0.999305,0.0001299281,0.00004180579,0.0001261246,0.0002634422,0.0001337238],"domain_scores_gemma":[0.9989825,0.0001357762,0.0002407312,0.00008307507,0.0001969391,0.0003609381],"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":[0.00005691755,0.00004397552,0.0004480564,0.00002004426,0.00001733851,0.0005608571,0.000293198,0.001155386,0.002031905,0.992466,0.0004472858,0.002458997],"study_design_scores_gemma":[0.00007034128,0.00008772567,0.001104161,0.00001957161,0.00002524286,0.00102712,0.0002692879,0.01125404,0.001260656,0.9807763,0.004057895,0.00004771868],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8838516,0.0007897382,0.05798479,0.00133607,0.0004439859,0.0000913601,0.0001618545,0.0001844947,0.05515615],"genre_scores_gemma":[0.9723498,0.0003628389,0.007999996,0.0002199628,0.0003738411,0.00004864779,0.0001364815,0.00007682197,0.01843164],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004737433,"threshold_uncertainty_score":0.01584828,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0356264298963502,"score_gpt":0.3098832553999262,"score_spread":0.274256825503576,"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."}}