{"id":"W4407107527","doi":"10.1007/s13398-025-01706-3","title":"Modular identities for some special cases of Ramanujan’s general continued fraction","year":2025,"lang":"es","type":"article","venue":"Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria","funders":"","keywords":"Ramanujan's sum; Fraction (chemistry); Modular design; Mathematics; Combinatorics; Computer science; Chemistry; Chromatography","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":["metaresearch","metaepi_narrow","research_integrity"],"consensus_categories":[],"category_scores_codex":[0.002383228,0.0009559778,0.002157886,0.0006127087,0.0004781065,0.0009111459,0.001171523,0.001742347,0.0002054349],"category_scores_gemma":[0.008719037,0.000950272,0.0008455906,0.0008031435,0.001382177,0.001531865,0.0005073489,0.002064319,0.00002930744],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001619938,"about_ca_system_score_gemma":0.0007275596,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000897053,"about_ca_topic_score_gemma":0.000006216242,"domain_scores_codex":[0.9935608,0.0007586729,0.00225307,0.000997041,0.0009321649,0.001498268],"domain_scores_gemma":[0.9900517,0.006620473,0.001440426,0.0009440405,0.0005744179,0.0003689255],"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":[0.000476995,0.000346101,0.0005575286,0.01014074,0.0004465343,0.0002273869,0.0006519944,0.00003558782,0.03229067,0.9454397,0.008382768,0.001003981],"study_design_scores_gemma":[0.002418335,0.0003425888,0.005093354,0.005005598,0.002582185,0.0006528479,0.002065855,0.004366002,0.05304375,0.8934201,0.02942409,0.001585317],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9754682,0.006503386,0.005199678,0.0006630216,0.00049819,0.002314341,0.0006205144,0.0003130135,0.008419667],"genre_scores_gemma":[0.955603,0.01019465,0.02090973,0.0003787589,0.002378588,0.0003405724,0.00008819752,0.0002027155,0.009903811],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05201963,"threshold_uncertainty_score":0.9996309,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01840323443200311,"score_gpt":0.3466197460060828,"score_spread":0.3282165115740797,"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."}}