{"id":"W2635647965","doi":"10.1093/imrn/rnz217","title":"The Image Size of Iterated Rational Maps over Finite Fields","year":2019,"lang":"en","type":"preprint","venue":"International Mathematics Research Notices","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Iterated function; Mathematics; Finite field; Image (mathematics); Modulo; Prime (order theory); Combinatorics; Discrete mathematics; Degree (music); Rational function; Number theory; Field (mathematics); Algebraic number field; Connection (principal bundle); Pure mathematics; Mathematical analysis; Geometry; 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":[0.001340082,0.0003290896,0.0006925189,0.002250848,0.0007735121,0.002665893,0.001145275,0.0006594738,0.003474418],"category_scores_gemma":[0.01281624,0.0004345475,0.0004048667,0.0005357195,0.002604591,0.003461555,0.001392381,0.0009375191,0.0002119114],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001858022,"about_ca_system_score_gemma":0.0005484748,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000909731,"about_ca_topic_score_gemma":0.0004655879,"domain_scores_codex":[0.9992071,0.0001544368,0.00003553111,0.0001641461,0.0002624007,0.0001764609],"domain_scores_gemma":[0.9896094,0.007428006,0.0009494782,0.0006868184,0.000589807,0.000736484],"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":[0.001718294,0.0003895324,0.03778898,0.0003901715,0.0001462891,0.001193677,0.0018763,0.05628457,0.06456441,0.7988591,0.00250643,0.03428233],"study_design_scores_gemma":[0.000156387,0.000389234,0.0302361,0.0001851743,0.0001781,0.001719185,0.001022141,0.3673449,0.07926295,0.5160319,0.003328928,0.0001450605],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.986585,0.0001554006,0.007646572,0.0002513419,0.00001172919,0.00001112157,0.00009037211,0.00008576062,0.005162563],"genre_scores_gemma":[0.9976963,0.0001077868,0.00128825,0.00001641381,0.00002671429,0.00001749548,0.00008749126,0.00002171809,0.0007377444],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003474418,"threshold_uncertainty_score":0.01348096,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06299207860439189,"score_gpt":0.3805312113339832,"score_spread":0.3175391327295913,"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."}}