{"id":"W2794152400","doi":"10.1016/j.jnt.2018.01.012","title":"Three Ramanujan continued fractions with modularity","year":2018,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"Toronto Metropolitan University","funders":"National Research Foundation of Korea; Ministry of Education","keywords":"Ramanujan's sum; Mathematics; Modularity (biology); Pure mathematics; Combinatorics; Arithmetic; Evolutionary biology","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0007667451,0.0001359594,0.0003450314,0.00005988515,0.0001215877,0.00004994545,0.0002265458,0.00006678707,0.003873658],"category_scores_gemma":[0.001247236,0.00009425972,0.000119691,0.0001123595,0.0003273868,0.0004062755,0.00004409719,0.0003291404,0.0001523661],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005319739,"about_ca_system_score_gemma":0.00004783791,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001930348,"about_ca_topic_score_gemma":0.00004251446,"domain_scores_codex":[0.9988286,0.00007769305,0.0004405995,0.00009586777,0.0003616969,0.0001955611],"domain_scores_gemma":[0.9974725,0.001091541,0.0005329148,0.0002934672,0.0005055472,0.0001040885],"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":[0.0003275333,0.0004252481,0.0005869373,0.00008010108,0.0003263502,0.0000787305,0.0009539058,0.000001611585,0.0003649695,0.9681724,0.02786,0.0008222038],"study_design_scores_gemma":[0.0005277838,0.0001310762,0.0004358387,0.0001735214,0.0001219418,0.0005047554,0.0005005117,0.00002498909,0.0008308687,0.9935637,0.003064682,0.0001202915],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2971161,0.00003481591,0.651002,0.0002759511,0.0003612564,0.0001734432,0.00001605653,0.00006459418,0.05095574],"genre_scores_gemma":[0.7787821,0.000007054449,0.2128985,0.0001444219,0.001086384,0.000007369069,9.615108e-7,0.00006853718,0.00700476],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.4816659,"threshold_uncertainty_score":0.9970369,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03789028672209517,"score_gpt":0.3389364646094095,"score_spread":0.3010461778873143,"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."}}