{"id":"W1970111813","doi":"10.1016/j.crma.2010.02.010","title":"A remark on the effective Mordell Conjecture and rational pre-images under quadratic dynamical systems","year":2010,"lang":"en","type":"article","venue":"Comptes Rendus Mathématique","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Mathematics; Conjecture; Inverse; Bounded function; Quadratic equation; Rational point; Combinatorics; Dynamical systems theory; Pure mathematics; Point (geometry); Periodic point; Orbit (dynamics); Mathematical analysis; Geometry; Physics","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":[0.0008318644,0.0003443214,0.000504632,0.00007393621,0.0002325549,0.0002543098,0.0002893907,0.0002645447,0.0004071211],"category_scores_gemma":[0.0011148,0.0002103628,0.0001023046,0.0001221142,0.000236835,0.00008712732,0.0001109914,0.0008439387,0.00007090372],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003969136,"about_ca_system_score_gemma":0.0000417571,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000159357,"about_ca_topic_score_gemma":0.00003279772,"domain_scores_codex":[0.9981589,0.0003090241,0.0004980629,0.0003618485,0.0003750339,0.0002970754],"domain_scores_gemma":[0.9926144,0.006289114,0.0002537228,0.0006078792,0.0001036427,0.0001312128],"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":[0.00002063681,0.000184733,0.00008296013,0.0003486919,0.0000798623,0.000005545747,0.0003544825,0.00006884661,0.003053662,0.991202,0.004463879,0.0001347283],"study_design_scores_gemma":[0.0004817993,0.0001780808,0.002386864,0.0003492186,0.00007845691,0.0001762406,0.0002099012,0.1974488,0.0005137307,0.7974265,0.0003018818,0.0004485814],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9377981,0.0001291961,0.04430136,0.002496746,0.0003698646,0.002123572,0.00008283072,0.0001825206,0.0125158],"genre_scores_gemma":[0.9936526,0.00001183818,0.004956285,0.0002121343,0.0001203021,0.00028475,0.00001936007,0.0000519448,0.0006907885],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1973799,"threshold_uncertainty_score":0.8578346,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01519232885882674,"score_gpt":0.2835457996623466,"score_spread":0.2683534708035198,"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."}}