{"id":"W4402831299","doi":"10.1080/00150517.2004.12428433","title":"Period Lengths of Continued Fractions Involving Fibonacci Numbers","year":2004,"lang":"en","type":"article","venue":"˜The œFibonacci quarterly","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"","keywords":"Fibonacci number; Period (music); Period length; Lucas number; Mathematics; Combinatorics; Physics; Discrete mathematics","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":[0.0001134679,0.0001845114,0.0002609338,0.00003053673,0.0003174088,0.00005131423,0.0002778053,0.00004142418,0.0004534149],"category_scores_gemma":[0.000004768511,0.0001446454,0.0001855821,0.0002199744,0.0001478996,0.000183034,0.00002580208,0.0002108411,0.0001386044],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002896316,"about_ca_system_score_gemma":0.00005649296,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002033289,"about_ca_topic_score_gemma":0.00004016267,"domain_scores_codex":[0.9989029,0.0000273461,0.0003892188,0.0002297083,0.0001682254,0.0002826123],"domain_scores_gemma":[0.9989349,0.0001778879,0.0002135112,0.000495112,0.00009359278,0.00008501449],"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":[0.00001507477,0.0002438823,0.0002623923,0.00001615239,0.00007711444,5.85235e-7,0.003118786,0.0001282536,0.002841273,0.9792413,0.0002408685,0.01381435],"study_design_scores_gemma":[0.001125759,0.0001594536,0.0006804237,0.00006079453,0.00007505715,0.000004948666,0.01685646,0.0001625406,0.001120547,0.9603479,0.01906568,0.0003404574],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5743818,0.0001854101,0.3629898,0.002346038,0.0003368793,0.001131828,0.0001821657,0.0001879056,0.05825816],"genre_scores_gemma":[0.9956157,0.000001405342,0.003192045,0.00005240069,0.0002106487,0.000117804,0.00002230527,0.00002715685,0.0007605169],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4212339,"threshold_uncertainty_score":0.5898467,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007299710553553625,"score_gpt":0.2554573010983085,"score_spread":0.2481575905447549,"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."}}