{"id":"W2091416417","doi":"10.1142/s1793042109002602","title":"A GENERALIZATION OF ROTH'S THEOREM IN FUNCTION FIELDS","year":2009,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Cardinality (data modeling); Combinatorics; Generalization; Degree (music); Finite field; Polynomial; Ring (chemistry); Zero (linguistics); Polynomial ring; Field (mathematics); Discrete mathematics; Function field; Function (biology); Pure mathematics; Mathematical analysis","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":[0.008234615,0.001583046,0.002826174,0.003963251,0.002435239,0.003527828,0.004033169,0.00230609,0.008175157],"category_scores_gemma":[0.01307465,0.0007673377,0.003733197,0.003586509,0.005992534,0.01641568,0.004850151,0.005701356,0.002677906],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002618361,"about_ca_system_score_gemma":0.001554363,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001198474,"about_ca_topic_score_gemma":0.0006504789,"domain_scores_codex":[0.9959484,0.0009761183,0.0002431435,0.001401637,0.000945867,0.0004848437],"domain_scores_gemma":[0.9931277,0.003560386,0.0005777846,0.001673826,0.0007472548,0.0003130301],"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":[0.00004023553,0.00001373687,0.0001886784,0.0001014893,0.00002129676,0.000108362,0.0001186277,0.001363763,0.00054797,0.9840531,0.004494879,0.008947894],"study_design_scores_gemma":[0.00003474416,0.00005700076,0.0003077039,0.00005252979,0.00004240096,0.0004340273,0.00005125631,0.009624299,0.001048721,0.9696778,0.01862577,0.0000437138],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04965758,0.00543298,0.7891898,0.007877099,0.002986045,0.0002483849,0.001753593,0.00129319,0.1415612],"genre_scores_gemma":[0.6114609,0.007706785,0.3181333,0.006061489,0.004683482,0.0005431414,0.001201309,0.0008997844,0.0493099],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008234615,"threshold_uncertainty_score":0.04354936,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008158623682477266,"score_gpt":0.2572963913296001,"score_spread":0.2491377676471229,"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."}}