{"id":"W2080886024","doi":"10.1112/s1461157009000187","title":"The Mordell–Weil sieve: proving non-existence of rational points on curves","year":2010,"lang":"en","type":"article","venue":"LMS Journal of Computation and Mathematics","topic":"Cryptography and Residue Arithmetic","field":"Computer Science","cited_by":53,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Sieve (category theory); Rational point; Algebra over a field; Genus; Rational number; Simple (philosophy)","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":[0.003651841,0.001294342,0.001938335,0.003920618,0.001810597,0.004563093,0.001362573,0.002065077,0.006246185],"category_scores_gemma":[0.01934015,0.0007479478,0.001335147,0.002330988,0.004833682,0.009210292,0.006736778,0.003974321,0.001623236],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001107542,"about_ca_system_score_gemma":0.0009257919,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003097494,"about_ca_topic_score_gemma":0.0003105246,"domain_scores_codex":[0.9972995,0.0006712695,0.0001731577,0.0003903482,0.0009669973,0.0004988007],"domain_scores_gemma":[0.992282,0.004573136,0.0004852856,0.001698015,0.0005498684,0.0004115997],"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":[0.000428988,0.0001186029,0.008357362,0.0003886237,0.0001540056,0.001489077,0.00116278,0.01604716,0.0145302,0.8738726,0.003012347,0.08043814],"study_design_scores_gemma":[0.00006526733,0.0001410258,0.001318233,0.0001551164,0.00005179997,0.0009936838,0.0004161723,0.05770024,0.04196375,0.8903767,0.006738006,0.00007989623],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.531112,0.0009064854,0.4275274,0.002153095,0.0002283526,0.0001080718,0.0002402809,0.001317027,0.03640717],"genre_scores_gemma":[0.9427683,0.0005874952,0.05137276,0.0002361119,0.000187096,0.00005161102,0.0002322309,0.0001832866,0.004381165],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006246185,"threshold_uncertainty_score":0.02089554,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008561974885662713,"score_gpt":0.2542585128835853,"score_spread":0.2456965379979226,"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."}}