{"id":"W2108077859","doi":"10.4153/cjm-2008-050-8","title":"Conjugate Reciprocal Polynomials with All Roots on the Unit Circle","year":2008,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"Pacific Institute for the Mathematical Sciences; Queen's University","funders":"","keywords":"Mathematics; Monic polynomial; Unit circle; Combinatorics; Degree (music); Reciprocal; Unit sphere; Discrete mathematics; Pure mathematics; Polynomial; 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":[0.0007955775,0.0005134272,0.0009948853,0.002474981,0.001284314,0.002733728,0.0008329675,0.0006370747,0.002500194],"category_scores_gemma":[0.004203395,0.0002940157,0.0005484947,0.0008369101,0.003209859,0.001781503,0.001977513,0.000903328,0.0003088306],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001175466,"about_ca_system_score_gemma":0.000334328,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007463547,"about_ca_topic_score_gemma":0.000293737,"domain_scores_codex":[0.9989767,0.0002035799,0.0000372725,0.0001884394,0.0004114498,0.0001825294],"domain_scores_gemma":[0.9982364,0.0005189193,0.0004890714,0.000205762,0.0002253661,0.0003243753],"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":[0.0002910671,0.00003575172,0.002599728,0.00005586746,0.00003402768,0.0005456627,0.000422536,0.008779158,0.009937536,0.9695528,0.0005052668,0.007240637],"study_design_scores_gemma":[0.000162396,0.0004043107,0.01135738,0.00005602236,0.00008655631,0.003628722,0.001251725,0.1108863,0.03058425,0.8325938,0.008837276,0.0001512757],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9620841,0.00024858,0.02741725,0.0001916484,0.00003386882,0.00001244898,0.00008587362,0.00006734399,0.009859093],"genre_scores_gemma":[0.9972754,0.00006928627,0.001555442,0.00001551067,0.00004003402,0.000008667796,0.00004501386,0.00001073681,0.0009799541],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002733728,"threshold_uncertainty_score":0.00852865,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0873642215421818,"score_gpt":0.2751163434503981,"score_spread":0.1877521219082163,"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."}}