{"id":"W2952097853","doi":"10.48550/arxiv.1407.5884","title":"A probabilistic approach to value sets of polynomials over finite fields","year":2014,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Infinity; Distribution (mathematics); Finite field; Order (exchange); Expected value; Polynomial; Value (mathematics); Combinatorics; Discrete mathematics; Degree (music); Random variable; Probabilistic logic; Set (abstract data type); Finite set; Field (mathematics); Random field; Pure mathematics; Statistics; Mathematical analysis; Physics; Computer science","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0005217709,0.0002858193,0.000434447,0.0003810283,0.00008821837,0.0000733331,0.002132254,0.000289407,0.00001724261],"category_scores_gemma":[0.0001095203,0.0003171863,0.0003188295,0.0006880643,0.0001046512,0.0001348053,0.002039154,0.0003814975,0.00002378302],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005396868,"about_ca_system_score_gemma":0.0001194023,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008109266,"about_ca_topic_score_gemma":0.00000593769,"domain_scores_codex":[0.99808,0.0002715963,0.0002427592,0.0009918219,0.0001050517,0.0003087315],"domain_scores_gemma":[0.9975805,0.0003179804,0.0002349984,0.001580983,0.0001028079,0.000182675],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00004194483,0.00013052,0.0003356796,0.0001583837,0.00006357113,0.00001062206,0.0004226863,0.372307,0.0000147929,0.6258045,0.0003036416,0.0004066926],"study_design_scores_gemma":[0.0004469322,0.0001746496,0.001490803,0.0001708635,0.00009935982,0.000002521678,0.00002321026,0.5934558,0.0001400899,0.4026952,0.0006672648,0.0006333579],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2833273,0.00001371653,0.7076247,0.00003865822,0.0003190144,0.0003249907,0.00001324462,0.0001202075,0.008218144],"genre_scores_gemma":[0.9945893,0.000008447836,0.004838773,0.00021313,0.00005044295,0.00000235742,0.0000060589,0.00001247399,0.0002790286],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.711262,"threshold_uncertainty_score":0.999928,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05612003960260158,"score_gpt":0.191049739230665,"score_spread":0.1349296996280634,"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."}}