{"id":"W1982203184","doi":"10.1112/jlms/jdq095","title":"On sums of sets of primes with positive relative density","year":2011,"lang":"en","type":"article","venue":"Journal of the London Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Natural density; Modulo; Multiplicative function; Natural number; Argument (complex analysis); Upper and lower bounds","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002026999,0.0008336027,0.001541216,0.002441423,0.00199835,0.003320933,0.001330897,0.0007109914,0.005162884],"category_scores_gemma":[0.01341513,0.0007539368,0.001029398,0.001824611,0.003725379,0.008548015,0.005278204,0.001814611,0.0005719335],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001075349,"about_ca_system_score_gemma":0.0003765413,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003370755,"about_ca_topic_score_gemma":0.0002778036,"domain_scores_codex":[0.9974093,0.0006921378,0.0001611588,0.0004325674,0.001056748,0.0002480723],"domain_scores_gemma":[0.9916477,0.006071305,0.0006423633,0.0005729921,0.0005189337,0.000546639],"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":[0.0001335515,0.00002495793,0.001305647,0.0001582611,0.00004240178,0.0004045817,0.0007148678,0.005271261,0.005334661,0.9748018,0.001014215,0.01079369],"study_design_scores_gemma":[0.00002290535,0.00006163907,0.001264082,0.00006435971,0.00005999528,0.0008887805,0.0003779836,0.03098607,0.004440145,0.9569399,0.004855641,0.00003850926],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6366731,0.002366413,0.2961235,0.001987007,0.0002922862,0.00008670907,0.0003606632,0.0004029115,0.06170753],"genre_scores_gemma":[0.9398599,0.001066726,0.04631224,0.0004035274,0.0005596608,0.0002542073,0.0004588229,0.0001667091,0.01091819],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005162884,"threshold_uncertainty_score":0.01727158,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05124494790039281,"score_gpt":0.3176475228096626,"score_spread":0.2664025749092698,"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."}}