{"id":"W2286891823","doi":"10.13140/2.1.1974.8486","title":"On the symmetry definitions for the constrained Hamiltonian systems","year":2014,"lang":"en","type":"article","venue":"arXiv (Cornell University)","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"","keywords":"Hamiltonian (control theory); Hamiltonian system; Symmetry (geometry); Dynamical systems theory; Physics; Theoretical physics; Mathematics; Mathematical physics; Statistical physics; Classical mechanics; Quantum mechanics; Mathematical optimization; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002263107,0.000116232,0.0001253024,0.00002683569,0.0004668048,0.00005882913,0.0002677116,0.00003376786,0.00006618782],"category_scores_gemma":[0.00001942757,0.00007003062,0.000143862,0.0001737378,0.0001261537,0.00004220886,0.00002928777,0.0001147574,0.00009291204],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002061398,"about_ca_system_score_gemma":0.00002026808,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000252034,"about_ca_topic_score_gemma":0.00001106048,"domain_scores_codex":[0.9993445,0.00008671153,0.0001048215,0.0002150714,0.00004066818,0.0002081739],"domain_scores_gemma":[0.9981496,0.001316422,0.00008000316,0.0003427077,0.00004905484,0.00006221818],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00001052059,0.00003237238,0.001090942,0.000005562922,0.00005542167,4.743644e-7,0.00001882447,0.006085736,0.0000140227,0.9919659,0.0006200282,0.0001002158],"study_design_scores_gemma":[0.0007851034,0.0001059073,0.0007223791,0.00004766708,0.00009786266,8.695023e-7,0.001379327,0.7896681,0.00001549098,0.1982258,0.008725764,0.0002256519],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4671403,0.0000155427,0.4768755,0.0005581646,0.0004957322,0.0007057796,0.0001564067,0.00006056291,0.05399197],"genre_scores_gemma":[0.998766,0.000001463493,0.000006838862,0.0001004891,0.0001691877,0.000006196933,0.00001146081,0.00001054093,0.0009278198],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.79374,"threshold_uncertainty_score":0.3590333,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06007168666998839,"score_gpt":0.1696260210347534,"score_spread":0.1095543343647651,"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."}}