{"id":"W4387641873","doi":"10.1142/s1793042124500234","title":"On the jth smallest modulus of a covering system with distinct moduli","year":2023,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"Fonds de recherche du Québec – Nature et technologies; Natural Sciences and Engineering Research Council of Canada; Courtois Foundation","keywords":"Moduli; Mathematics; Modulus; Bounded function; Constant (computer programming); Modular equation; Pure mathematics; Moduli space; Combinatorics; Mathematical analysis; Geometry; Moduli of algebraic curves; Computer science; Physics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001448171,0.0008675709,0.0009484464,0.002018639,0.0020211,0.002850557,0.00128827,0.00119002,0.009044393],"category_scores_gemma":[0.008192032,0.0004953508,0.0006999476,0.001362715,0.004559188,0.007273127,0.003640228,0.002835432,0.001438768],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00139078,"about_ca_system_score_gemma":0.0005746402,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000515789,"about_ca_topic_score_gemma":0.0004317251,"domain_scores_codex":[0.9992261,0.0001716131,0.00004175806,0.0002343735,0.0001728944,0.0001533246],"domain_scores_gemma":[0.9946674,0.003431381,0.0005927148,0.000346998,0.0003471647,0.000614345],"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":[0.0001175026,0.0000171984,0.0008470109,0.0001364206,0.00001499041,0.000126847,0.0004150602,0.001364772,0.003156351,0.9842499,0.002458249,0.007095583],"study_design_scores_gemma":[0.00002662277,0.00005663438,0.001130232,0.00007357136,0.00003239665,0.0003452562,0.0001391994,0.009668736,0.002445122,0.9774848,0.008547408,0.00005002473],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6723021,0.006615053,0.1722463,0.007321076,0.001187766,0.0000919189,0.0008248705,0.0004886343,0.1389223],"genre_scores_gemma":[0.9508816,0.001572471,0.03490987,0.000538796,0.001026925,0.0001278885,0.0004909657,0.0002266673,0.01022483],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009044393,"threshold_uncertainty_score":0.03025645,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02570177866368628,"score_gpt":0.2884431693469132,"score_spread":0.2627413906832269,"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."}}