{"id":"W4407958612","doi":"10.1016/j.jde.2025.02.051","title":"Response tori in Hamiltonian systems of high order degeneracy - the super-critical case","year":2025,"lang":"en","type":"article","venue":"Journal of Differential Equations","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada; Natural Science Foundation of Shandong Province; Jilin University; Department of Science and Technology of Jilin Province; National Natural Science Foundation of China; University of Alberta","keywords":"Mathematics; Torus; Degeneracy (biology); Hamiltonian system; Order (exchange); Hamiltonian (control theory); Mathematical physics; Pure mathematics; Mathematical analysis; Geometry; Mathematical optimization","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006157306,0.0006524576,0.001408762,0.001668116,0.001923599,0.002667929,0.001338325,0.002003667,0.009828998],"category_scores_gemma":[0.002766267,0.0006582682,0.000545392,0.0004695363,0.003781344,0.002490978,0.002193461,0.001560425,0.0005488647],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009627935,"about_ca_system_score_gemma":0.0006159102,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001271162,"about_ca_topic_score_gemma":0.001050274,"domain_scores_codex":[0.9996371,0.0001060605,0.00001374313,0.00003950058,0.0000794982,0.0001241362],"domain_scores_gemma":[0.9986336,0.0003737791,0.000200393,0.0001517324,0.0001233311,0.0005171706],"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":[0.0004463442,0.0002263378,0.001545356,0.0001705347,0.00005974309,0.001587525,0.0007107226,0.04774316,0.01290545,0.9286238,0.002865663,0.003115252],"study_design_scores_gemma":[0.0001182275,0.00006991267,0.001933206,0.00002504695,0.00001641386,0.0003981709,0.000546199,0.4137096,0.000822881,0.5816625,0.0006349763,0.00006288585],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9199771,0.0005512917,0.02210971,0.002471112,0.0002656437,0.0001143418,0.0001637329,0.0004480963,0.05389902],"genre_scores_gemma":[0.9936354,0.0001301459,0.001673156,0.0001458364,0.00008485196,0.00003684439,0.00005400354,0.00006381202,0.004175919],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009828998,"threshold_uncertainty_score":0.0328812,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01148646801265789,"score_gpt":0.2874073630554969,"score_spread":0.275920895042839,"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."}}