{"id":"W2799509695","doi":"10.1016/j.jnt.2018.03.007","title":"Non-isotrivial elliptic surfaces with non-zero average root number","year":2018,"lang":"en","type":"preprint","venue":"Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Root (linguistics); Zero (linguistics); Elliptic curve; Rank (graph theory); Degree (music); Combinatorics; Pure mathematics; Discrete mathematics; Physics","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","research_integrity","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.005143657,0.001078729,0.002040384,0.0002832726,0.0002730399,0.0002522186,0.001679283,0.000959916,0.01843755],"category_scores_gemma":[0.0007530249,0.0008104922,0.0009238031,0.0004239003,0.0006383185,0.0004292786,0.0008378679,0.003012589,0.001605758],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000271639,"about_ca_system_score_gemma":0.0006617421,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001045939,"about_ca_topic_score_gemma":0.000008939203,"domain_scores_codex":[0.9942946,0.000725571,0.001897806,0.0007047658,0.001474409,0.0009028444],"domain_scores_gemma":[0.9913241,0.002561698,0.003183586,0.001414543,0.001015262,0.0005008103],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.02419658,0.009362335,0.1213804,0.01022377,0.02380361,0.007410884,0.03006021,0.002455933,0.0006057202,0.1289212,0.6363242,0.005255122],"study_design_scores_gemma":[0.002298014,0.0003574807,0.002089771,0.002452487,0.001041646,0.002355574,0.0003615712,0.0000705547,0.001387055,0.9823433,0.004021395,0.0012212],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9140805,0.0001136484,0.02644169,0.0001201716,0.002762879,0.000542768,0.0001051484,0.00007928126,0.0557539],"genre_scores_gemma":[0.9743807,0.00007215116,0.0111302,0.0001634837,0.002744505,0.00002188851,0.00002538208,0.0002591199,0.01120262],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.853422,"threshold_uncertainty_score":0.9994346,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01932148204460453,"score_gpt":0.2882142952025766,"score_spread":0.2688928131579721,"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."}}