{"id":"W4416710514","doi":"10.1090/mbk/154/29","title":"The Prime Number Theorem for arithmetic progressions","year":2025,"lang":"en","type":"book-chapter","venue":"American Mathematical Society eBooks","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Prime number; Prime (order theory); Algebra over a field; Fermat number; Natural number","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.001985635,0.0007646807,0.001347697,0.0000407293,0.0009345856,0.0002157575,0.001233536,0.0004052678,0.0005290227],"category_scores_gemma":[0.001302968,0.0004866989,0.001738952,0.00007468833,0.003987599,0.0000277601,0.0006056196,0.00115392,0.0003211504],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000286256,"about_ca_system_score_gemma":0.0004979378,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000351174,"about_ca_topic_score_gemma":0.000003767099,"domain_scores_codex":[0.9959988,0.0001216272,0.0010535,0.0007573739,0.00105504,0.001013662],"domain_scores_gemma":[0.9845322,0.01240961,0.0007086039,0.001638635,0.0004066582,0.0003043141],"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":[0.00003574393,0.00006306224,0.000001269158,0.0004277947,0.0008901973,0.00000316179,0.000471942,1.990413e-8,0.000003991813,0.9245417,0.04301855,0.03054254],"study_design_scores_gemma":[0.0002793235,0.00008115056,2.361886e-7,0.0006003391,0.0005324376,0.00001630561,0.0005221163,0.0005397071,0.00004086584,0.8723163,0.1246037,0.0004674862],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.00001793007,0.000072788,0.04430795,0.001200416,0.00008400379,0.002793175,0.0000870443,0.0002933357,0.9511433],"genre_scores_gemma":[0.000487971,0.00004331893,0.06757954,0.0003390115,0.0002574365,0.0006458171,0.00001296165,0.0002332129,0.9304007],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.08158517,"threshold_uncertainty_score":0.9997585,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0389112937944363,"score_gpt":0.3574407024916733,"score_spread":0.318529408697237,"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."}}