{"id":"W3104905942","doi":"","title":"Variation of the root number in families of elliptic curves","year":2019,"lang":"en","type":"article","venue":"cIRcle (University of British Columbia)","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Conjecture; Square-free integer; Geometry of numbers; Combinatorics; Degree (music); Elliptic curve; Multiplicative function; Number theory; Discriminant; Pure mathematics; Discrete mathematics; Mathematical analysis; Geometry","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":[0.0003601135,0.00003076855,0.000269746,0.00002877718,0.00003376925,0.000005440455,0.0002903073,0.00007480257,0.0004543636],"category_scores_gemma":[0.0001100144,0.0000808335,0.0001078181,0.000383443,0.00015656,0.000150535,0.000108659,0.00009365952,0.00001574853],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002428211,"about_ca_system_score_gemma":0.00004262492,"about_ca_topic_candidate":true,"about_ca_topic_consensus":true,"about_ca_topic_score_codex":0.01624398,"about_ca_topic_score_gemma":0.03437692,"domain_scores_codex":[0.9992566,0.000102633,0.0001682728,0.0001425493,0.0002196872,0.0001102645],"domain_scores_gemma":[0.9991232,0.0002043694,0.0002404035,0.0003018029,0.0001098171,0.00002039016],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.00003715586,0.0008407463,0.9550494,0.004195508,0.0001732201,0.00001067391,0.003297922,0.00002722224,0.00178619,0.002120521,0.0015973,0.03086413],"study_design_scores_gemma":[0.0005319103,0.00002258067,0.9681422,0.000675489,0.00003674978,0.000007554198,0.001431201,0.00003160385,0.00001349627,0.02901339,0.00001863741,0.0000752312],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9938044,0.00007058033,0.0001139028,0.00003186451,0.00009236908,0.0002298412,0.00003645148,0.00001070505,0.005609862],"genre_scores_gemma":[0.9982529,0.00005942482,0.0002282399,0.000009716224,0.000005036791,1.69606e-7,0.000002143777,0.000006837799,0.001435524],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0307889,"threshold_uncertainty_score":0.9903069,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008493061549366245,"score_gpt":0.1903604554364256,"score_spread":0.1818673938870594,"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."}}