{"id":"W4414603052","doi":"10.5539/jmr.v17n3p25","title":"On Families of Irreducible Polynomials With Constraints on Height, Mahler Measure, and Graeffe Transforms","year":2025,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Discrete orthogonal polynomials; Difference polynomials; Integer (computer science); Classical orthogonal polynomials; Wilson polynomials; Orthogonal polynomials; Hahn polynomials","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001526932,0.0005087371,0.0005889348,0.001774919,0.001670958,0.001338602,0.0006600549,0.0007208366,0.002907417],"category_scores_gemma":[0.007123671,0.0003676365,0.0006485587,0.001047574,0.003070127,0.003146347,0.001662485,0.001458416,0.0003596975],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001267396,"about_ca_system_score_gemma":0.0005223,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008701041,"about_ca_topic_score_gemma":0.0006648562,"domain_scores_codex":[0.999143,0.0002201279,0.00002793511,0.0001078388,0.0002827104,0.0002182553],"domain_scores_gemma":[0.9963946,0.002162181,0.0005253915,0.000291977,0.000248547,0.0003772868],"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":[0.00004323746,0.00001453379,0.0006689074,0.00002584507,0.000005987887,0.000180214,0.0002929408,0.004594441,0.001765058,0.9881632,0.0004831528,0.003762563],"study_design_scores_gemma":[0.00002747714,0.00004437764,0.00120306,0.00003231327,0.00001171896,0.0004580335,0.0002330715,0.03956626,0.00170317,0.9537181,0.002967985,0.00003441793],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8362652,0.0009173532,0.1255196,0.001111417,0.00006442022,0.00002771147,0.0002217794,0.0001642745,0.03570836],"genre_scores_gemma":[0.9786829,0.0005964477,0.01626738,0.0001103567,0.000122885,0.00003426625,0.0001731513,0.00005151986,0.003961097],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002907417,"threshold_uncertainty_score":0.009726286,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1209779386393324,"score_gpt":0.4072079911972228,"score_spread":0.2862300525578904,"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."}}