{"id":"W2000961504","doi":"10.1016/j.jnt.2014.12.002","title":"On the nature of e and non-vanishing of derivatives of L-series at s= 1/2","year":2014,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Transcendental number; Series (stratigraphy); Transcendence (philosophy); Pure mathematics; Dirichlet series; Quadratic equation; Character (mathematics); Dirichlet distribution; Mathematical analysis; Geometry; Theology; 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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.003700662,0.0001270995,0.0005067772,0.00007709189,0.00005749051,0.00001003631,0.0003768737,0.0001126231,0.0009206876],"category_scores_gemma":[0.004733766,0.0000744668,0.0001604529,0.0001398441,0.0005438328,0.0001455969,0.0001489822,0.0004763247,0.000003072537],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002587826,"about_ca_system_score_gemma":0.00004752546,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000129405,"about_ca_topic_score_gemma":0.000002506757,"domain_scores_codex":[0.9980778,0.000550314,0.0006142475,0.00008743459,0.0005232251,0.0001469528],"domain_scores_gemma":[0.990979,0.007268311,0.001012801,0.0003145603,0.0003673071,0.00005797725],"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":[0.0008967101,0.0001940001,0.002628998,0.0003392659,0.0003449752,0.000004904764,0.003386448,0.000004294413,0.009288172,0.9784857,0.003929173,0.0004973568],"study_design_scores_gemma":[0.0004904499,0.000252256,0.001401382,0.0005252233,0.00007015371,0.00008888492,0.002087071,0.00003247079,0.04321852,0.9514711,0.0002865982,0.00007584156],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9796674,0.00007390719,0.001056445,0.0002765604,0.00004842576,0.00008587439,0.00001467739,0.000002616986,0.01877413],"genre_scores_gemma":[0.9969102,0.00003310795,0.001886188,0.0000500212,0.0000619097,8.632201e-7,3.297742e-7,0.00002160607,0.001035829],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03393034,"threshold_uncertainty_score":0.9999926,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02446865008330839,"score_gpt":0.3262290671820136,"score_spread":0.3017604170987052,"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."}}