{"id":"W2093579744","doi":"10.1142/s179304211250159x","title":"A NOTE ON BARKER POLYNOMIALS","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Mathematics; Degree (music); Combinatorics; Polynomial; Irreducibility; Integer (computer science); Discrete mathematics; Pure mathematics","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":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.001727604,0.0001283284,0.0002481981,0.0001193186,0.00003681613,0.0000414521,0.0003392961,0.00007332964,0.02421289],"category_scores_gemma":[0.002183179,0.00009256217,0.0002365283,0.00005133326,0.00004444374,0.0002456874,0.00004649583,0.0002155219,0.0007880871],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009534294,"about_ca_system_score_gemma":0.00004294592,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001110615,"about_ca_topic_score_gemma":2.923036e-7,"domain_scores_codex":[0.9984732,0.0001784835,0.0005856726,0.0000668335,0.0005004572,0.0001953299],"domain_scores_gemma":[0.9961324,0.002898477,0.0004122922,0.0001602854,0.0002431739,0.0001533142],"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":[0.0004661375,0.0006299293,0.0004875753,0.00001254448,0.0003433898,0.00001915677,0.0007513877,0.00000161416,0.0006465981,0.8486682,0.1383865,0.00958706],"study_design_scores_gemma":[0.0008800559,0.00009734834,0.000625666,0.0002438593,0.00009581316,0.0008362134,0.000167194,0.000009203458,0.003128811,0.760757,0.2329395,0.0002193184],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4903432,0.0001804925,0.04491923,0.003080186,0.01282178,0.0002947267,0.0002316899,0.00008041081,0.4480483],"genre_scores_gemma":[0.9807948,0.00001015757,0.0101485,0.000916781,0.003049865,0.000004893887,0.000002707182,0.0000301593,0.00504209],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4904517,"threshold_uncertainty_score":0.9999899,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04222491879312153,"score_gpt":0.3700040092684516,"score_spread":0.32777909047533,"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."}}