{"id":"W4377028142","doi":"10.1017/s0004972723000412","title":"DIOPHANTINE EQUATIONS OF THE FORM OVER FUNCTION FIELDS","year":2023,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Subring; Mathematics; Diophantine equation; Prime (order theory); Field (mathematics); Polynomial; Combinatorics; Ring (chemistry); Degree (music); Prime number; Function field; Function (biology); Finite field; Polynomial ring; Integer (computer science); Mathematical analysis; Pure mathematics; Physics","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":[0.0006251298,0.0008015548,0.0009005209,0.001012515,0.001073486,0.001657439,0.0006901658,0.001227115,0.004091383],"category_scores_gemma":[0.002664495,0.0003277893,0.0007679105,0.001066168,0.00139323,0.001749625,0.001421243,0.001669287,0.0004004091],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001464001,"about_ca_system_score_gemma":0.0007572204,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001967178,"about_ca_topic_score_gemma":0.001606411,"domain_scores_codex":[0.9995741,0.00008522634,0.00003007758,0.0000700239,0.000137295,0.0001033673],"domain_scores_gemma":[0.9993241,0.000325233,0.0001310983,0.00003922858,0.00009302649,0.00008741215],"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":[0.0001875196,0.0001466414,0.002814142,0.0001928712,0.00006708682,0.0007697848,0.0009565119,0.02660066,0.008594814,0.9458062,0.002550812,0.01131292],"study_design_scores_gemma":[0.0002860917,0.0002238501,0.002725066,0.0001331611,0.000059596,0.0009381782,0.001531088,0.1656038,0.006683751,0.8071872,0.01454445,0.00008380036],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8764645,0.001603807,0.0747292,0.002750804,0.0003785613,0.0001057856,0.0004039318,0.00008868043,0.04347471],"genre_scores_gemma":[0.9591273,0.000792892,0.01624718,0.0002438677,0.0002218731,0.00007330671,0.0002538349,0.00003666931,0.02300308],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004091383,"threshold_uncertainty_score":0.01368701,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04228019019068398,"score_gpt":0.2901466713194616,"score_spread":0.2478664811287777,"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."}}