{"id":"W4413062718","doi":"10.1215/00127094-2024-0055","title":"An almost sharp quantitative version of the Duffin–Schaeffer conjecture","year":2025,"lang":"en","type":"article","venue":"Duke Mathematical Journal","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Conjecture; Mathematics; Pure mathematics","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001211786,0.0002743051,0.0006444505,0.0001358415,0.0002948932,0.0001154998,0.0007789952,0.0001989372,0.001219316],"category_scores_gemma":[0.002300117,0.0001573522,0.0003587727,0.0003810595,0.0002500036,0.0001729928,0.0001839265,0.0006702468,0.00005199564],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006609027,"about_ca_system_score_gemma":0.0001176755,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001414524,"about_ca_topic_score_gemma":0.000002463,"domain_scores_codex":[0.9976114,0.0002546922,0.000935554,0.0002256189,0.0006176813,0.0003550297],"domain_scores_gemma":[0.9967268,0.001762736,0.0004332125,0.0006464254,0.0002611714,0.0001696221],"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":[0.00004564095,0.0005783002,0.0001031869,0.0004516415,0.0001248094,0.00001111094,0.0007195122,0.00001356621,0.002133974,0.9923365,0.003068235,0.0004135878],"study_design_scores_gemma":[0.0006572219,0.0001428189,0.0002631899,0.000784981,0.000168876,0.0001187522,0.0005868791,0.01821922,0.001711221,0.9765662,0.000599555,0.0001810707],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6435516,0.00014104,0.3003189,0.003731478,0.000587045,0.0008574516,0.00006988218,0.00008153354,0.05066113],"genre_scores_gemma":[0.9524861,0.00001471863,0.04577549,0.0003275506,0.00006876196,0.00001139924,0.000002878853,0.00003998643,0.001273113],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3089345,"threshold_uncertainty_score":0.9996937,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02418470148972546,"score_gpt":0.344459261580363,"score_spread":0.3202745600906375,"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."}}