{"id":"W3100709352","doi":"","title":"Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space","year":2013,"lang":"en","type":"article","venue":"","topic":"Algebraic and Geometric Analysis","field":"Mathematics","cited_by":35,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dalhousie University; University of Waterloo","funders":"","keywords":"Invariant (physics); Euclidean space; Separable space; Euclidean geometry; Mathematics; Pure mathematics; Seven-dimensional space; Hamiltonian system; Hamiltonian (control theory); Euclidean group; Algebra over a field; Mathematical analysis; Euclidean distance matrix; Mathematical physics; Geometry; Affine space; Mathematical optimization","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":[0.0008398636,0.0003686336,0.0005558517,0.002003593,0.0007791195,0.001808056,0.000724746,0.0007559072,0.003504652],"category_scores_gemma":[0.001651389,0.0002044307,0.0003430453,0.0007063783,0.002358255,0.002377806,0.001072445,0.0008931358,0.0002518054],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009993126,"about_ca_system_score_gemma":0.0004600451,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001069856,"about_ca_topic_score_gemma":0.0006645597,"domain_scores_codex":[0.9994221,0.0001595353,0.00003002543,0.00007697587,0.0001854223,0.000126073],"domain_scores_gemma":[0.9992925,0.0001602281,0.0001799382,0.00009446845,0.0001272973,0.0001456112],"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":[0.00001083812,0.00001200184,0.0002170818,0.0000114187,0.000003842815,0.00003232488,0.00006224344,0.00140248,0.0006632864,0.9955036,0.0003939705,0.001687038],"study_design_scores_gemma":[0.00001931256,0.0000216062,0.0006036648,0.000009381021,0.000003936188,0.00006938568,0.00008499414,0.04489225,0.0005786407,0.9528831,0.0008187225,0.00001503957],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8753356,0.0005972403,0.09198485,0.0007827756,0.0001687878,0.00003550734,0.0002476943,0.0001400338,0.03070745],"genre_scores_gemma":[0.9897647,0.0001582617,0.006185811,0.00007583073,0.00008787428,0.00001826043,0.0001889481,0.00002658347,0.00349383],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003504652,"threshold_uncertainty_score":0.01172429,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04155889112241785,"score_gpt":0.2824257254297915,"score_spread":0.2408668343073737,"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."}}