{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002162524,0.000470609,0.0006700398,0.002205824,0.0008276902,0.001985323,0.001058989,0.0004935104,0.005085576],"category_scores_gemma":[0.02035509,0.0004807653,0.0005781972,0.001032788,0.003634331,0.00402645,0.001617183,0.001724581,0.0005705204],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001331085,"about_ca_system_score_gemma":0.0004678948,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004916862,"about_ca_topic_score_gemma":0.000361932,"domain_scores_codex":[0.9988629,0.0002793192,0.00004718032,0.000218524,0.000308534,0.0002836713],"domain_scores_gemma":[0.9899625,0.006130258,0.001463702,0.0008857017,0.0008888249,0.0006688705],"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":[0.0001938951,0.00003554462,0.00307049,0.00009796568,0.00002252938,0.0002292476,0.000350487,0.01659571,0.007692825,0.9608571,0.0009613973,0.009892918],"study_design_scores_gemma":[0.00001758965,0.00007947079,0.003693647,0.0000545595,0.00001967877,0.0004067309,0.0001317454,0.09339999,0.006081081,0.8942593,0.00179668,0.00005961302],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6292083,0.0007592555,0.3478916,0.001029062,0.0001149702,0.00004236754,0.0003323164,0.0003613414,0.02026082],"genre_scores_gemma":[0.9920297,0.0001822166,0.005817975,0.00005755548,0.000150851,0.00003387535,0.00007021405,0.00005047023,0.001607065],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005085576,"threshold_uncertainty_score":0.01701301,"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."}}