{"id":"W2566344843","doi":"10.1002/cpa.21791","title":"Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line","year":2018,"lang":"en","type":"preprint","venue":"Communications on Pure and Applied Mathematics","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Critical line; Conjecture; Riemann hypothesis; Mathematics; Order (exchange); Riemann zeta function; Interval (graph theory); Line (geometry); Combinatorics; Real line; Function (biology); Measure (data warehouse); Mathematical physics; Physics; Mathematical analysis; Geometry; Condensed matter physics","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":[0.001293237,0.0003031034,0.0006273637,0.00009360916,0.0002827062,0.00004265314,0.002742092,0.0003093902,0.00006002502],"category_scores_gemma":[0.001083156,0.0001793363,0.0002796644,0.0002416152,0.00155739,0.00001899349,0.004131233,0.001243899,0.00001535718],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005145445,"about_ca_system_score_gemma":0.0001128241,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002594515,"about_ca_topic_score_gemma":0.00002051505,"domain_scores_codex":[0.9978138,0.0002134801,0.0008570279,0.0002818785,0.00062134,0.0002124351],"domain_scores_gemma":[0.990505,0.002441668,0.0004237526,0.00625401,0.0003147718,0.00006083154],"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":[0.00005347353,0.001169581,0.00003566487,0.001436883,0.0002174574,8.430455e-8,0.001111696,0.00001006197,0.0002001607,0.9930356,0.001992253,0.000737087],"study_design_scores_gemma":[0.0001522015,0.00008918669,0.00005686971,0.001294314,0.0004230037,0.000004194022,0.0005423865,0.001894193,0.002279038,0.992739,0.0003616911,0.0001639414],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5242719,0.0008393007,0.07590222,0.02233687,0.00111807,0.01005862,0.0008080468,0.0003210205,0.364344],"genre_scores_gemma":[0.9804599,0.00006934024,0.01862108,0.0001204747,0.00006787646,0.0001510242,0.00001279564,0.0000584203,0.0004390592],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4561881,"threshold_uncertainty_score":0.7313123,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.126523805870953,"score_gpt":0.3862704317494766,"score_spread":0.2597466258785236,"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."}}