{"id":"W4387772467","doi":"10.1007/978-3-031-37238-4_6","title":"Cubic Extensions of the Lucas Sequences","year":2023,"lang":"en","type":"book-chapter","venue":"CMS/CAIMS books in mathematics","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Lucas sequence; Key (lock); Lucas number; Mathematics; Computer science; Calculus (dental); Epistemology; Mathematical economics; Philosophy; Combinatorics; Medicine; Fibonacci number","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":[0.0002157903,0.0004005884,0.0003297394,0.001251212,0.0009863292,0.001741499,0.0003840965,0.0003653989,0.02020651],"category_scores_gemma":[0.001179516,0.0002384687,0.00031591,0.001481494,0.001114546,0.001626728,0.000871707,0.002011253,0.002740001],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001474357,"about_ca_system_score_gemma":0.0009080743,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003546417,"about_ca_topic_score_gemma":0.00490741,"domain_scores_codex":[0.9998105,0.0000300606,0.000007299489,0.00002686573,0.00008840385,0.00003681922],"domain_scores_gemma":[0.9997318,0.0000650361,0.00003487409,0.00003607521,0.00008214915,0.00004997497],"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":[0.00001627072,0.000005950488,0.00004583503,0.00002628367,0.000001196829,0.00002979751,0.00009180667,0.0004238241,0.0003357244,0.9787602,0.004962968,0.01530011],"study_design_scores_gemma":[0.00001332759,0.00001571978,0.0003275434,0.00002447258,0.000003170355,0.0001261653,0.0001161625,0.001937841,0.0003378033,0.9166292,0.08045802,0.00001058512],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"methods","genre_scores_codex":[0.05645896,0.004345993,0.03349596,0.00165651,0.0008011638,0.00004095813,0.0004569766,0.0002733214,0.9024702],"genre_scores_gemma":[0.5621874,0.004851062,0.02290761,0.0005514869,0.00115028,0.00007458639,0.0006469468,0.0002271894,0.4074035],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.02020651,"threshold_uncertainty_score":0.06759751,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03455168237967889,"score_gpt":0.2819112606444969,"score_spread":0.247359578264818,"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."}}