{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001164784,0.0002534047,0.0005896777,0.0001992684,0.0002794568,0.00008067589,0.0005796795,0.0001236298,0.0004068828],"category_scores_gemma":[0.001577876,0.0001544117,0.0001707948,0.0002085438,0.0002969108,0.0001074927,0.00001799571,0.0004930742,0.00008683925],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001051452,"about_ca_system_score_gemma":0.0007437252,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001224356,"about_ca_topic_score_gemma":0.002187252,"domain_scores_codex":[0.9979554,0.00009232116,0.0008457245,0.0001387963,0.0004890873,0.0004786622],"domain_scores_gemma":[0.9962339,0.001595523,0.0006723207,0.0005208392,0.0003002956,0.0006771204],"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":[0.00005383383,0.0004622237,0.0003933025,0.0003635206,0.0005717294,0.001452912,0.00527341,0.00006923745,0.0002273241,0.9606016,0.02990646,0.0006244869],"study_design_scores_gemma":[0.001597213,0.001121455,0.001204724,0.001445244,0.0003468781,0.005775353,0.002084025,0.002420628,0.0009795041,0.971776,0.01041585,0.0008331384],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9605151,0.00007622065,0.01572845,0.003689897,0.000186859,0.0004918096,0.00003662501,0.00002280623,0.01925217],"genre_scores_gemma":[0.9765487,0.00002031248,0.02153402,0.0008331931,0.0001333827,0.000007650264,0.000001330471,0.00007491841,0.000846485],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01949061,"threshold_uncertainty_score":0.6296727,"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."}}