{"id":"W1542673380","doi":"10.37236/4822","title":"Hyperbinary Expansions and Stern Polynomials","year":2015,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Combinatorics; Integer (computer science); Sequence (biology); Polynomial; Class (philosophy); Function (biology); Generating function; Stern; Difference polynomials; Discrete mathematics; Orthogonal polynomials; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.002098138,0.00021768,0.0004979976,0.0001071507,0.0001290264,0.00004465685,0.0005678809,0.00009384792,0.000004353805],"category_scores_gemma":[0.001345397,0.0001446809,0.0001072058,0.0002865426,0.0001061866,0.000249048,0.0001606193,0.0007294833,0.000006731259],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003119485,"about_ca_system_score_gemma":0.0005479903,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002282723,"about_ca_topic_score_gemma":0.000001397882,"domain_scores_codex":[0.9978696,0.0002177768,0.0006679327,0.0001199782,0.0005989502,0.000525728],"domain_scores_gemma":[0.9972779,0.0009882248,0.0006822137,0.0004204786,0.0004199666,0.0002112666],"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":[0.00007367959,0.0001982789,0.0000581961,0.00002145738,0.00007969078,0.0000146716,0.0009739801,0.00000607013,0.000222727,0.9961944,0.001889685,0.0002671937],"study_design_scores_gemma":[0.00163644,0.0008694322,0.00001414769,0.00005065123,0.0001306902,0.0007086806,0.0008151647,0.00004852472,0.0007644897,0.9917125,0.003090295,0.0001590218],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9719355,0.006111042,0.0171537,0.001289663,0.001542845,0.0003135722,0.00000112391,0.00005455661,0.001597977],"genre_scores_gemma":[0.9984166,0.0003558846,0.0004157202,0.00005450354,0.0002041809,0.00000412698,1.836522e-7,0.00004676234,0.0005020197],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0264811,"threshold_uncertainty_score":0.5899915,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05986491884891614,"score_gpt":0.321807746312308,"score_spread":0.2619428274633918,"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."}}