{"id":"W3092729066","doi":"10.1112/plms.12542","title":"Moments of moments of primes in arithmetic progressions","year":2023,"lang":"en","type":"article","venue":"Proceedings of the London Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; University of Ottawa","keywords":"Mathematics; Conjecture; Riemann hypothesis; Mathematical proof; Independence (probability theory); Range (aeronautics); Distribution (mathematics); Gaussian; Limiting; Combinatorics; Pure mathematics; Mathematical analysis; Statistics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002005142,0.0001870974,0.0006607376,0.0001033481,0.000057387,0.0000133365,0.0007918222,0.0001362703,0.0001183678],"category_scores_gemma":[0.001759416,0.0001223445,0.0004033555,0.001355372,0.0005070574,0.0001077481,0.0006876382,0.0002840539,0.00001507986],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007232674,"about_ca_system_score_gemma":0.0000526581,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004408809,"about_ca_topic_score_gemma":2.675025e-7,"domain_scores_codex":[0.9973246,0.0000204834,0.0009050587,0.0002379783,0.001093707,0.0004181447],"domain_scores_gemma":[0.9981413,0.0006816419,0.0005273119,0.0002662742,0.0003004923,0.00008290364],"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":[0.0001626766,0.004764491,0.09421595,0.02521631,0.001004957,0.000001706876,0.02394517,0.000009062989,0.1104929,0.7193737,0.01983828,0.0009748028],"study_design_scores_gemma":[0.0007921275,0.00007071225,0.002180944,0.001275023,0.00008850044,0.000002789897,0.002934639,0.003381114,0.07806447,0.9110579,0.00001745874,0.0001342499],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.995542,0.00002502518,0.0000670906,0.0004693718,0.0000230075,0.0008232365,0.00001140957,0.00004686876,0.002991948],"genre_scores_gemma":[0.9865711,0.00002829893,0.01030205,0.00001061932,0.00001511982,0.00007521576,7.797495e-7,0.00004088773,0.002955965],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1916842,"threshold_uncertainty_score":0.4989063,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05215784226918484,"score_gpt":0.3559246532809086,"score_spread":0.3037668110117237,"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."}}