{"id":"W3105800061","doi":"","title":"Non-existence of Ramanujan congruences in modular forms of level four","year":2012,"lang":"en","type":"article","venue":"","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Congruence relation; Mathematics; Ramanujan's sum; Modulo; Modular form; Pure mathematics; Crank; Generating function; Ramanujan tau function; Combinatorics; Inverse; Theta function; Geometry","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":[0.001874409,0.0008243942,0.0009275366,0.002709271,0.002629357,0.00286176,0.001015169,0.001185216,0.005783349],"category_scores_gemma":[0.005848435,0.0006820406,0.001041965,0.0009262454,0.00563473,0.00278539,0.002293666,0.001841808,0.0007287178],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001128709,"about_ca_system_score_gemma":0.0007906454,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005606902,"about_ca_topic_score_gemma":0.0005418505,"domain_scores_codex":[0.9985274,0.0003519807,0.00008745532,0.0002010811,0.000487149,0.0003447987],"domain_scores_gemma":[0.9981078,0.0005498069,0.0002952899,0.0002100759,0.0002748907,0.0005621371],"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":[0.00008690471,0.00005294337,0.001175807,0.00002926888,0.000009131482,0.0003891691,0.0005642739,0.0006322766,0.004910459,0.9886478,0.0005000245,0.003001955],"study_design_scores_gemma":[0.00009898847,0.00008072596,0.001207337,0.00002047562,0.0000109495,0.0005143672,0.0002144921,0.006580933,0.00304375,0.9867952,0.001399584,0.00003321531],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9433198,0.0001492743,0.01998499,0.0005254958,0.0001686522,0.00007022991,0.00006437496,0.0001104758,0.03560669],"genre_scores_gemma":[0.9881363,0.00008291884,0.006251005,0.0001220111,0.0001751713,0.00006737397,0.00006980362,0.00004332085,0.005052172],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005783349,"threshold_uncertainty_score":0.01934725,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1597985348372519,"score_gpt":0.3594001915211159,"score_spread":0.1996016566838639,"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."}}