{"id":"W2069622828","doi":"10.4153/cmb-2007-023-2","title":"Elliptic <i>K</i>3 Surfaces with Geometric Mordell–Weil Rank 15","year":2007,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":27,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Rank (graph theory); Elliptic curve; Pure mathematics; Combinatorics; Algebra over a field","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003141078,0.0006140735,0.0003979491,0.00110127,0.001492427,0.002988615,0.0004471541,0.0005359274,0.00800095],"category_scores_gemma":[0.0005357271,0.0002809354,0.0006155596,0.0005482882,0.001852184,0.001599221,0.002109255,0.001498389,0.001034118],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001064289,"about_ca_system_score_gemma":0.0003630908,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007599544,"about_ca_topic_score_gemma":0.0005585603,"domain_scores_codex":[0.999754,0.0000332338,0.00001305611,0.00003120991,0.00008335891,0.00008517554],"domain_scores_gemma":[0.9997647,0.00004070497,0.00005162327,0.00003401553,0.00004462065,0.00006434818],"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":[0.00009081108,0.00002302045,0.002283994,0.00007846433,0.00001993676,0.0006265651,0.0007026307,0.002172982,0.009075728,0.9681516,0.003436671,0.01333761],"study_design_scores_gemma":[0.00005421075,0.0001040875,0.007177865,0.00007131238,0.00005657275,0.00212846,0.001389466,0.01045198,0.02206342,0.8975888,0.05883779,0.00007595082],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7693614,0.0003730978,0.02855436,0.001035671,0.0002237787,0.00004538651,0.000299047,0.0004790028,0.1996283],"genre_scores_gemma":[0.9839706,0.0001147799,0.005665891,0.00008621358,0.00003811589,0.00001184245,0.0001194146,0.00004994848,0.009943328],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00800095,"threshold_uncertainty_score":0.02676582,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01720158165682047,"score_gpt":0.2397851435549185,"score_spread":0.222583561898098,"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."}}