{"id":"W4402997304","doi":"10.1112/mtk.12281","title":"A discrete mean value of the Riemann zeta function","year":2024,"lang":"en","type":"article","venue":"Mathematika","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Lethbridge","funders":"Natural Sciences and Engineering Research Council of Canada; Austrian Science Fund; Agence Nationale de la Recherche; Pacific Institute for the Mathematical Sciences; University of Lethbridge","keywords":"Mathematics; Riemann zeta function; Pure mathematics; Value (mathematics); Riemann hypothesis; Riemann Xi function; Mathematical analysis; Statistics","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":[0.0009099437,0.00013996,0.0002292177,0.00008244337,0.0000648772,0.00005005109,0.0003478885,0.0000602074,0.001745327],"category_scores_gemma":[0.0003111016,0.00008169272,0.0002045615,0.0003877713,0.0001415882,0.00007768151,0.0001785971,0.0001849988,0.0005164453],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003771791,"about_ca_system_score_gemma":0.0000466007,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001044033,"about_ca_topic_score_gemma":0.00001086356,"domain_scores_codex":[0.9986507,0.0001253808,0.0003058752,0.0002126547,0.0004918618,0.0002135808],"domain_scores_gemma":[0.998652,0.000495395,0.00007963127,0.0006819668,0.00004100602,0.00004997292],"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":[0.000008375709,0.00003972308,0.00003654028,0.0006376011,0.0001232221,0.00000353648,0.001248613,0.000001438485,0.0006416198,0.9878634,0.009009231,0.0003866508],"study_design_scores_gemma":[0.00009999772,0.00002257594,0.00005390516,0.0003851386,0.0001245435,0.00002063563,0.0003522633,0.003666606,0.001467692,0.9899406,0.003766168,0.00009981375],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.1623936,0.0005553573,0.1095679,0.001605034,0.0005852379,0.001245407,0.00002927428,0.0006138219,0.7234043],"genre_scores_gemma":[0.9025328,0.000003574962,0.002900345,0.00002319657,0.00009270736,0.00002668429,9.23015e-7,0.00009108016,0.09432872],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7401392,"threshold_uncertainty_score":0.9991672,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04328213145676837,"score_gpt":0.3386189098392238,"score_spread":0.2953367783824555,"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."}}