{"id":"W2947012397","doi":"10.1093/qmathj/haz043","title":"HIGHER CORRELATIONS AND THE ALTERNATIVE HYPOTHESIS","year":2020,"lang":"en","type":"article","venue":"The Quarterly Journal of Mathematics","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Counterexample; Riemann zeta function; Riemann hypothesis; Function (biology); Stationary ergodic process; Alternative hypothesis; Ergodic theory","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":[],"consensus_categories":[],"category_scores_codex":[0.002173419,0.000153932,0.0004318447,0.00004505058,0.0001824982,0.00009927453,0.0006423002,0.0000433012,0.0002446169],"category_scores_gemma":[0.001013689,0.00006959887,0.0001836565,0.0001838194,0.0004785447,0.0001327428,0.00004706697,0.0004688606,0.00006639178],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002348179,"about_ca_system_score_gemma":0.00004298438,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002643087,"about_ca_topic_score_gemma":0.000001230421,"domain_scores_codex":[0.9980468,0.0003984306,0.0006798369,0.00008904179,0.0005962403,0.0001896123],"domain_scores_gemma":[0.9916802,0.007006227,0.000669362,0.0002984531,0.0002205959,0.0001251454],"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":[0.0002024088,0.0001493805,0.00003346272,0.0001257061,0.0006308969,0.00002680365,0.07091031,0.000014542,0.0000634419,0.9165385,0.007475377,0.003829124],"study_design_scores_gemma":[0.001438421,0.0002436762,0.00002881097,0.00006982563,0.0003118447,0.0001867223,0.009942039,0.005522576,0.00004482294,0.9816534,0.0004648587,0.00009302818],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6778247,0.001593694,0.1846508,0.1132062,0.0005581297,0.001675231,0.00002274018,0.00009599136,0.02037248],"genre_scores_gemma":[0.9860091,0.0000550596,0.011877,0.0004681168,0.0004722139,0.000006234278,1.077714e-7,0.00004048523,0.001071708],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3081843,"threshold_uncertainty_score":0.283816,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09650276976652356,"score_gpt":0.3244777332547909,"score_spread":0.2279749634882673,"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."}}