{"id":"W1671624764","doi":"10.3390/math11020262","title":"Principal Solutions of Recurrence Relations and Irrationality Questions in Number Theory","year":2023,"lang":"en","type":"article","venue":"Mathematics","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Recurrence relation; Irrational number; Irrationality; Mathematics; Relation (database); Term (time); Principal (computer security); Integer (computer science); Transcendence (philosophy); Series (stratigraphy); Pure mathematics; Combinatorics; Epistemology; Philosophy; Quantum mechanics; Computer science; Physics","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":[0.001307977,0.0005572829,0.0005704478,0.001461889,0.001038598,0.00169667,0.0006875156,0.0007793917,0.002791059],"category_scores_gemma":[0.005081185,0.0002425557,0.0006132588,0.001079043,0.0032878,0.003261387,0.001487587,0.001994151,0.0006104375],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001095904,"about_ca_system_score_gemma":0.0004086769,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003766086,"about_ca_topic_score_gemma":0.0003768144,"domain_scores_codex":[0.9993081,0.0002437798,0.00005141132,0.0001198858,0.0001898112,0.00008694467],"domain_scores_gemma":[0.9986283,0.000617057,0.0002425168,0.0001433457,0.0002666848,0.0001021838],"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":[0.000009977559,0.000006765333,0.0001205527,0.00003150146,0.000002928131,0.00007697075,0.0003481647,0.0007119564,0.0009021997,0.9917515,0.0004053608,0.005632084],"study_design_scores_gemma":[0.00000652162,0.0000173057,0.00007548444,0.00001234921,0.000003977374,0.0001315195,0.0001032901,0.004844458,0.0007551843,0.9906418,0.003398934,0.000009091692],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4296997,0.006665542,0.4391305,0.005177014,0.0008348149,0.00006471755,0.0001026418,0.0003188944,0.1180062],"genre_scores_gemma":[0.9305856,0.002247464,0.04597315,0.0004466908,0.0008189964,0.00007680533,0.00008415015,0.00009805908,0.01966913],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002791059,"threshold_uncertainty_score":0.009337008,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08992257985001159,"score_gpt":0.3424510323888925,"score_spread":0.2525284525388809,"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."}}