{"id":"W2971476823","doi":"10.4153/s0008439520000089","title":"Limiting Properties of the Distribution of Primes in an Arbitrarily Large Number of Residue Classes","year":2020,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Modulo; Invertible matrix; Logarithm; Congruence (geometry); Distribution (mathematics); Prime number; Number theory; Integer (computer science)","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"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":[0.005385768,0.0006414524,0.001647492,0.003375478,0.001823586,0.003636287,0.002446352,0.001005449,0.005347739],"category_scores_gemma":[0.03262735,0.0007670274,0.0007686481,0.001129401,0.007060455,0.006564495,0.003482784,0.002727504,0.0005318082],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00282875,"about_ca_system_score_gemma":0.0008198407,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008869232,"about_ca_topic_score_gemma":0.0003538968,"domain_scores_codex":[0.9981772,0.0005097224,0.00006496104,0.0004093365,0.0005619098,0.0002769302],"domain_scores_gemma":[0.9842406,0.01014798,0.001428442,0.001428209,0.001072035,0.001682606],"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":[0.000199118,0.00006822512,0.004002677,0.00009146086,0.00002328142,0.0003329956,0.0003147653,0.006491011,0.003975492,0.9777777,0.001259984,0.00546336],"study_design_scores_gemma":[0.000118352,0.0001245688,0.003437006,0.00008564829,0.00003815845,0.001152162,0.0002807768,0.1950328,0.007358689,0.7888291,0.003463652,0.00007912731],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8374928,0.0008213254,0.1296456,0.002345632,0.0000958258,0.00008356218,0.0003094404,0.0004493979,0.02875637],"genre_scores_gemma":[0.9905865,0.0003558072,0.005234939,0.000141477,0.0001531487,0.00009819705,0.0001699696,0.00006675333,0.003193209],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005385768,"threshold_uncertainty_score":0.02848303,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0636419895049434,"score_gpt":0.3025600693644978,"score_spread":0.2389180798595543,"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."}}