{"id":"W2067656436","doi":"10.4153/cmb-2007-036-0","title":"Global Injectivity of<i>C</i><sup>1</sup>Maps of the Real Plane, Inseparable Leaves and the Palais–Smale Condition","year":2007,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Conselho Nacional de Desenvolvimento Científico e Tecnológico; Ministerio de Educación, Cultura y Deporte; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior; Fundação de Amparo à Pesquisa do Estado de São Paulo; Canadian Mathematical Society","keywords":"Mathematics; Converse; Jacobian matrix and determinant; Pure mathematics; Point (geometry); Plane (geometry); Component (thermodynamics); Mathematical analysis; Applied mathematics; Geometry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009107365,0.0001628873,0.0004305964,0.00004651439,0.0001707491,0.00002273655,0.0002218227,0.0001321703,0.0003934793],"category_scores_gemma":[0.001165713,0.0000961222,0.0001180046,0.0002185886,0.0005967268,0.00002794352,0.00005581311,0.0001423758,0.00004989334],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000106856,"about_ca_system_score_gemma":0.0000963262,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003581863,"about_ca_topic_score_gemma":0.007827398,"domain_scores_codex":[0.9984859,0.0001568128,0.0005723978,0.0001784495,0.000281892,0.0003245829],"domain_scores_gemma":[0.9976106,0.001479619,0.0002291472,0.000387011,0.00008786055,0.000205786],"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":[0.0000582715,0.00007386075,0.001564529,0.0002658022,0.0000439107,0.000002882825,0.0004951407,0.00005761156,0.00003429935,0.9951984,0.001842486,0.0003628466],"study_design_scores_gemma":[0.001477685,0.00006428645,0.003672737,0.0002778214,0.0001192797,0.00004376317,0.0008547528,0.00213034,0.0002486237,0.9885226,0.002352916,0.0002351228],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9398127,0.00005603178,0.02237124,0.0008593612,0.00006220157,0.0008527162,0.0003253199,0.00002569277,0.03563471],"genre_scores_gemma":[0.9981117,0.000005379803,0.001209309,0.00007128109,0.00004053843,0.00001642352,0.00000909043,0.00001350176,0.0005227802],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05829897,"threshold_uncertainty_score":0.541473,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01285267106678467,"score_gpt":0.2578748667022092,"score_spread":0.2450221956354245,"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."}}