{"id":"W4300056268","doi":"10.48550/arxiv.1803.06539","title":"The Graph Structure of Chebyshev Polynomials over Finite Fields and\\n Applications","year":2018,"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":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Chebyshev polynomials; Mathematics; Chebyshev filter; Graph; Chebyshev nodes; Chebyshev equation; Gegenbauer polynomials; Finite field; Discrete mathematics; Orthogonal polynomials; Applied mathematics; Classical orthogonal polynomials; Pure mathematics; Combinatorics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001832318,0.0001801362,0.0001917389,0.0001572202,0.0002858623,0.00008942526,0.001524285,0.0002208936,0.00002380685],"category_scores_gemma":[0.00001922977,0.0001572825,0.000166526,0.0005023677,0.0003257715,0.0001175203,0.00133045,0.0003175788,0.000003696962],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001475724,"about_ca_system_score_gemma":0.00006072479,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003122568,"about_ca_topic_score_gemma":0.00004622369,"domain_scores_codex":[0.998952,0.0001029309,0.0001541701,0.0005435447,0.00005907955,0.0001882812],"domain_scores_gemma":[0.9980792,0.0003219114,0.0002259862,0.00119981,0.00009738978,0.0000756517],"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":[0.0000320021,0.00002652609,0.00203035,0.00004875616,0.0001246123,0.000004325531,0.0002741882,0.00298516,0.0001234455,0.9914139,0.0003487334,0.002588008],"study_design_scores_gemma":[0.000237012,0.00005574035,0.003195175,0.00004177173,0.00006847986,0.000001749944,0.00004377803,0.01122902,0.000697466,0.9804901,0.003641836,0.000297861],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.322227,0.0002106866,0.67534,0.00008459467,0.0003284238,0.0003103022,0.00003884945,0.00009847664,0.001361627],"genre_scores_gemma":[0.9989635,0.0002716244,0.0004361748,0.00007330474,0.00008933908,0.000001074876,0.000003715057,0.000006481108,0.0001547717],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6767365,"threshold_uncertainty_score":0.6413796,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02886546373519731,"score_gpt":0.1801391196399248,"score_spread":0.1512736559047275,"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."}}