{"id":"W2952983018","doi":"10.48550/arxiv.1306.1657","title":"Limiting distributions of the classical error terms of prime number theory","year":2013,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Lethbridge","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Prime number theorem; Corollary; Limiting; Prime (order theory); Prime number; Term (time); Function (biology); Analytic number theory; Class (philosophy); Distribution (mathematics); Multiplicative number theory; Prime factor; Discrete mathematics; Pure mathematics; Combinatorics; Mathematical analysis; Computer science; Physics; Quantum mechanics","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":[0.0006835765,0.0002603392,0.0005316593,0.0000802476,0.0001228122,0.00001796012,0.001310272,0.0003315202,0.002432112],"category_scores_gemma":[0.001142738,0.0002081656,0.0005163642,0.0003894235,0.0009435727,0.00008299446,0.00217273,0.0008887055,0.0001007429],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001885484,"about_ca_system_score_gemma":0.0002161345,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003417509,"about_ca_topic_score_gemma":0.0000144208,"domain_scores_codex":[0.997985,0.0005887952,0.0004001577,0.0004779496,0.0001981979,0.0003498926],"domain_scores_gemma":[0.9958445,0.00167746,0.0006264292,0.001449755,0.0002831144,0.0001186757],"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":[0.00004584752,0.0002604779,0.007275216,0.0002760811,0.0002895034,0.00001237031,0.0001636612,0.000196676,0.0001249674,0.9894429,0.001832797,0.00007954012],"study_design_scores_gemma":[0.0002946239,0.00001596637,0.001315077,0.000379771,0.0003203715,0.000004487658,0.0003301461,0.007595168,0.001396069,0.9879407,0.0001808144,0.0002267533],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9234175,0.000005692631,0.03627351,0.0001300314,0.0001422698,0.0006639316,0.0005758983,0.00006503939,0.0387261],"genre_scores_gemma":[0.9823951,0.000007781054,0.0004031369,0.000006057979,0.00004770025,0.000002268081,0.00002686892,0.00003149762,0.01707966],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0589775,"threshold_uncertainty_score":0.9984798,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1394348675161561,"score_gpt":0.2676792527636401,"score_spread":0.128244385247484,"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."}}