{"id":"W1894786397","doi":"10.18910/11059","title":"Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences","year":2005,"lang":"en","type":"article","venue":"Osaka City University (Osaka City University)","topic":"Sports Dynamics and Biomechanics","field":"Engineering","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Power series; Series (stratigraphy); Algebraic number; Product (mathematics); Infinite product; Algebraic equation; Independence (probability theory); Pure mathematics; Mathematical analysis; Algebra over a field; Nonlinear system; Geometry; Statistics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002079454,0.0002736909,0.0003610498,0.0002963404,0.0002243992,0.00001805674,0.0006019094,0.0002618248,0.00008147771],"category_scores_gemma":[0.00003571554,0.0002843966,0.00009727162,0.001473919,0.0003718342,0.0007623976,0.0003368303,0.0003524518,0.00000181338],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001772558,"about_ca_system_score_gemma":0.0001600707,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003046799,"about_ca_topic_score_gemma":0.0009329357,"domain_scores_codex":[0.9986556,0.00007601411,0.000217271,0.0003855716,0.0003543571,0.0003112246],"domain_scores_gemma":[0.9988916,0.0000310106,0.00018464,0.000442454,0.00032353,0.000126757],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0056751,0.003538744,0.2970243,0.003077089,0.004489897,0.0008209303,0.02276366,0.0184741,0.3958608,0.1965924,0.03048368,0.02119928],"study_design_scores_gemma":[0.004619071,0.0008893142,0.035138,0.0005367748,0.0007574619,0.0001479786,0.006998865,0.01865894,0.1845197,0.0005325637,0.7440809,0.003120442],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9953434,0.0001040338,0.0003204041,0.0003723039,0.0002315872,0.0002422939,0.0003576878,0.000119765,0.002908564],"genre_scores_gemma":[0.9923246,0.0008770202,0.0010008,0.00001659425,0.00002677097,6.311826e-8,0.00004734872,0.00001617263,0.005690655],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7135972,"threshold_uncertainty_score":0.9999608,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005807953473838106,"score_gpt":0.1548781899456857,"score_spread":0.1490702364718476,"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."}}