{"id":"W2167958081","doi":"10.1142/s1793042114500171","title":"Analogues of Ramanujan's 24 squares formula","year":2014,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Ramanujan's sum; Mathematics; Ramanujan tau function; Combinatorics; Ramanujan theta function; Integer (computer science); Divisor function; Class (philosophy); Pure mathematics; Divisor (algebraic 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":[0.0008119483,0.0004963557,0.0005655864,0.001372135,0.001051594,0.001468055,0.00106325,0.0007470289,0.009222123],"category_scores_gemma":[0.002986937,0.0002325571,0.0006329764,0.0008977893,0.002094746,0.002487911,0.001088442,0.001479946,0.001378602],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009393825,"about_ca_system_score_gemma":0.0005406087,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005095959,"about_ca_topic_score_gemma":0.0004230991,"domain_scores_codex":[0.9992542,0.0001575409,0.00003051112,0.0001383277,0.0003285223,0.00009089794],"domain_scores_gemma":[0.9993223,0.0002467388,0.00009326688,0.0001227341,0.0001484032,0.00006654471],"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":[0.00001526917,0.000009773707,0.00007778931,0.00001631881,0.000002735383,0.00007209199,0.00009689729,0.0006401672,0.001042322,0.9903023,0.000893229,0.00683099],"study_design_scores_gemma":[0.00001179783,0.00002539469,0.0002393022,0.00001421525,0.00000459054,0.0002162792,0.00006292438,0.005741722,0.001163826,0.9805652,0.01193282,0.00002199743],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3384604,0.002398962,0.2239,0.002118995,0.001198927,0.0001308397,0.0003658177,0.0003769694,0.4310492],"genre_scores_gemma":[0.8654382,0.001002007,0.06498238,0.000752115,0.0007261841,0.0001147199,0.0001909682,0.0002623204,0.06653111],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009222123,"threshold_uncertainty_score":0.03085107,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03094206815979081,"score_gpt":0.3544654712320555,"score_spread":0.3235234030722647,"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."}}