{"id":"W1542087700","doi":"10.1090/s0002-9947-06-04171-7","title":"Partial hyperbolicity or dense elliptic periodic points for 𝐶¹-generic symplectic diffeomorphisms","year":2006,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":23,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"National Science Foundation","keywords":"Symplectic geometry; Diffeomorphism; Mathematics; Conjecture; Pure mathematics; Algorithm","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":[0.0005384982,0.0003696069,0.0009703581,0.00003857502,0.0004289609,0.00005575226,0.0005192705,0.0001117888,0.0005367871],"category_scores_gemma":[0.0003509638,0.0002318736,0.001176277,0.0006068853,0.001030001,0.00008327862,0.00003580125,0.0002738438,0.00002171159],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000117303,"about_ca_system_score_gemma":0.00008809428,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007163346,"about_ca_topic_score_gemma":0.00002538576,"domain_scores_codex":[0.997474,0.0001218346,0.0009343838,0.0003668747,0.0005258635,0.0005770986],"domain_scores_gemma":[0.9963146,0.00205929,0.0005499647,0.0007965127,0.0001394019,0.0001402346],"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":[0.001016225,0.01501278,0.0005592605,0.008714772,0.002366147,0.000009196657,0.006231746,0.001276724,0.0537111,0.894002,0.01028274,0.006817283],"study_design_scores_gemma":[0.001138792,0.0004008992,0.000463458,0.0001699255,0.001028117,0.00008798246,0.0006426566,0.1298774,0.005014468,0.8601854,0.0003692624,0.0006216877],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4283161,0.00001265988,0.5696674,0.0007695684,0.00006446099,0.0007472096,0.00009745476,0.00008548961,0.0002395852],"genre_scores_gemma":[0.8878635,0.00001693959,0.1103641,0.0002069388,0.00009548961,0.0002320277,0.000004271975,0.00008039751,0.001136402],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.4595473,"threshold_uncertainty_score":0.9455532,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0324528932219817,"score_gpt":0.2878056017359588,"score_spread":0.2553527085139771,"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."}}